diff --git a/docs/apidocs/qiskit.optimization.algorithms.rst b/docs/apidocs/qiskit.optimization.algorithms.rst
new file mode 100644
index 0000000000..bb7ba4dcc0
--- /dev/null
+++ b/docs/apidocs/qiskit.optimization.algorithms.rst
@@ -0,0 +1,6 @@
+.. _qiskit-optimization-algorithms:
+
+.. automodule:: qiskit.optimization.algorithms
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:
diff --git a/docs/apidocs/qiskit.optimization.applications.ising.rst b/docs/apidocs/qiskit.optimization.applications.ising.rst
new file mode 100644
index 0000000000..ff1ebb7629
--- /dev/null
+++ b/docs/apidocs/qiskit.optimization.applications.ising.rst
@@ -0,0 +1,6 @@
+.. _qiskit-optimization-applications-ising:
+
+.. automodule:: qiskit.optimization.applications.ising
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:
diff --git a/docs/apidocs/qiskit.optimization.applications.rst b/docs/apidocs/qiskit.optimization.applications.rst
new file mode 100644
index 0000000000..a388e86ad5
--- /dev/null
+++ b/docs/apidocs/qiskit.optimization.applications.rst
@@ -0,0 +1,6 @@
+.. _qiskit-optimization-applications:
+
+.. automodule:: qiskit.optimization.applications
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:
diff --git a/docs/apidocs/qiskit.optimization.converters.rst b/docs/apidocs/qiskit.optimization.converters.rst
new file mode 100644
index 0000000000..f51be315d4
--- /dev/null
+++ b/docs/apidocs/qiskit.optimization.converters.rst
@@ -0,0 +1,6 @@
+.. _qiskit-optimization-converters:
+
+.. automodule:: qiskit.optimization.converters
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:
diff --git a/docs/apidocs/qiskit.optimization.problems.rst b/docs/apidocs/qiskit.optimization.problems.rst
new file mode 100644
index 0000000000..3147fb929a
--- /dev/null
+++ b/docs/apidocs/qiskit.optimization.problems.rst
@@ -0,0 +1,6 @@
+.. _qiskit-optimization-problems:
+
+.. automodule:: qiskit.optimization.problems
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:
diff --git a/qiskit/optimization/__init__.py b/qiskit/optimization/__init__.py
index e302d95922..b3fec6bd07 100644
--- a/qiskit/optimization/__init__.py
+++ b/qiskit/optimization/__init__.py
@@ -18,22 +18,75 @@
 
 .. currentmodule:: qiskit.optimization
 
-Contents
-========
+Qiskit Optimization covers the whole stack from high-level modeling of optimization
+problems, with automatic conversion of problems to different required representations,
+to a suite of easy-to-use quantum optimization algorithms that are ready to run on
+classical simulators, as well as on real quantum devices via Qiskit.
+
+Qiskit Optimization enables easy, efficient modeling of optimization problems using `docplex
+<https://developer.ibm.com/docloud/documentation/optimization-modeling/modeling-for-python/>`_
+A uniform interface as well as automatic conversion between different problem representations
+allows users to solve problems using a large set of algorithms, from variational quantum algorithms,
+such as the Quantum Approximate Optimization Algorithm
+(:class:`~qiskit.aqua.algorithms.QAOA`), to
+`Grover Adaptive Search <https://arxiv.org/abs/quant-ph/9607014>`_
+(:class:`~algorithms.GroverOptimizer`), leveraging
+fundamental :mod:`~qiskit.aqua.algorithms` provided by Qiskit Aqua. Furthermore, the modular design
+of Qiskit Optimization allows it to be easily extended and facilitates rapid development and
+testing of new algorithms. Compatible classical optimizers are also provided for testing,
+validation, and benchmarking.
+
+Qiskit Optimization supports Quadratically Constrained Quadratic Programs – for simplicity we refer
+to them just as Quadratic Programs – with binary, integer, and continuous variables, as well as
+equality and inequality constraints. This class of optimization problems has a vast amount of
+relevant applications, while still being efficiently representable by matrices and vectors.
+This class covers some very interesting sub-classes, from Convex Continuous Quadratic Programs,
+which can be solved efficiently by classical optimization algorithms, to Quadratic Unconstrained
+Binary Optimization QUBO) problems, which cover many NP-complete, i.e., classically intractable,
+problems.
 
 .. autosummary::
    :toctree: ../stubs/
    :nosignatures:
 
     QuadraticProgram
+
+Representation of a Quadratically Constrained Quadratic Program supporting inequality and
+equality constraints as well as continuous, binary, and integer variables.
+
+.. autosummary::
+   :toctree: ../stubs/
+   :nosignatures:
+
     QiskitOptimizationError
+
+In addition to standard Python errors Qiskit Optimization will raise this error if circumstances
+are that it cannot proceed to completion.
+
+.. autosummary::
+   :toctree: ../stubs/
+   :nosignatures:
+
     INFINITY
 
+A constant for infinity.
+
+Submodules
+==========
+
+.. autosummary::
+   :toctree:
+
+   algorithms
+   applications
+   converters
+   problems
+
 """
 
 from .infinity import INFINITY  # must be at the top of the file
 from .exceptions import QiskitOptimizationError
-from .problems import QuadraticProgram
+from .problems.quadratic_program import QuadraticProgram
 from ._logging import (get_qiskit_optimization_logging,
                        set_qiskit_optimization_logging)
 
diff --git a/qiskit/optimization/algorithms/__init__.py b/qiskit/optimization/algorithms/__init__.py
index 4ede3a37cd..b793a1aef4 100644
--- a/qiskit/optimization/algorithms/__init__.py
+++ b/qiskit/optimization/algorithms/__init__.py
@@ -13,11 +13,10 @@
 # that they have been altered from the originals.
 
 """
-===================================================================
-Optimization stack for Aqua (:mod:`qiskit.optimization.algorithms`)
-===================================================================
+Optimization algorithms (:mod:`qiskit.optimization.algorithms`)
+===============================================================
 
-Algorithms for optimization algorithms.
+Algorithms for optimization problems.
 
 .. currentmodule:: qiskit.optimization.algorithms
 
diff --git a/qiskit/optimization/algorithms/admm_optimizer.py b/qiskit/optimization/algorithms/admm_optimizer.py
index bbb20897f5..ab3c3a9a73 100644
--- a/qiskit/optimization/algorithms/admm_optimizer.py
+++ b/qiskit/optimization/algorithms/admm_optimizer.py
@@ -19,12 +19,13 @@
 from typing import List, Optional, Any
 
 import numpy as np
-from qiskit.optimization import QiskitOptimizationError
-from qiskit.optimization.algorithms.cplex_optimizer import CplexOptimizer
-from qiskit.optimization.algorithms.optimization_algorithm import (OptimizationAlgorithm,
-                                                                   OptimizationResult)
-from qiskit.optimization.converters import IntegerToBinary
-from qiskit.optimization.problems import QuadraticProgram, Variable, Constraint, QuadraticObjective
+from ..exceptions import QiskitOptimizationError
+from .cplex_optimizer import CplexOptimizer
+from .optimization_algorithm import OptimizationAlgorithm, OptimizationResult
+from ..problems.quadratic_program import QuadraticProgram
+from ..problems.variable import Variable
+from ..problems.constraint import Constraint
+from ..problems.quadratic_objective import QuadraticObjective
 
 UPDATE_RHO_BY_TEN_PERCENT = 0
 UPDATE_RHO_BY_RESIDUALS = 1
@@ -251,6 +252,7 @@ def solve(self, problem: QuadraticProgram) -> ADMMOptimizationResult:
         self._log.debug("Initial problem: %s", problem.export_as_lp_string())
 
         # map integer variables to binary variables
+        from ..converters.integer_to_binary import IntegerToBinary
         int2bin = IntegerToBinary()
         problem = int2bin.encode(problem)
 
diff --git a/qiskit/optimization/algorithms/cobyla_optimizer.py b/qiskit/optimization/algorithms/cobyla_optimizer.py
index 36c5141e5c..2bdb0afe17 100644
--- a/qiskit/optimization/algorithms/cobyla_optimizer.py
+++ b/qiskit/optimization/algorithms/cobyla_optimizer.py
@@ -20,13 +20,15 @@
 import numpy as np
 from scipy.optimize import fmin_cobyla
 
-from qiskit.optimization.algorithms import OptimizationAlgorithm, OptimizationResult
-from qiskit.optimization.problems import QuadraticProgram, Constraint
-from qiskit.optimization import QiskitOptimizationError, INFINITY
+from .optimization_algorithm import OptimizationAlgorithm, OptimizationResult
+from ..problems.quadratic_program import QuadraticProgram
+from ..problems.constraint import Constraint
+from ..exceptions import QiskitOptimizationError
+from ..infinity import INFINITY
 
 
 class CobylaOptimizer(OptimizationAlgorithm):
-    """The SciPy COBYLA optimizer wrapped as an Qiskit ``OptimizationAlgorithm``.
+    """The SciPy COBYLA optimizer wrapped as an Qiskit :class:`OptimizationAlgorithm`.
 
     This class provides a wrapper for ``scipy.optimize.fmin_cobyla``
     (https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.fmin_cobyla.html)
@@ -34,6 +36,8 @@ class CobylaOptimizer(OptimizationAlgorithm):
     The arguments for ``fmin_cobyla`` are passed via the constructor.
 
     Examples:
+        >>> from qiskit.optimization.problems import QuadraticProgram
+        >>> from qiskit.optimization.algorithms import CobylaOptimizer
         >>> problem = QuadraticProgram()
         >>> # specify problem here
         >>> optimizer = CobylaOptimizer()
diff --git a/qiskit/optimization/algorithms/cplex_optimizer.py b/qiskit/optimization/algorithms/cplex_optimizer.py
index 6966aa0da3..ff29f827d6 100644
--- a/qiskit/optimization/algorithms/cplex_optimizer.py
+++ b/qiskit/optimization/algorithms/cplex_optimizer.py
@@ -33,12 +33,14 @@
 
 
 class CplexOptimizer(OptimizationAlgorithm):
-    """The CPLEX optimizer wrapped as an Qiskit ``OptimizationAlgorithm``.
+    """The CPLEX optimizer wrapped as an Qiskit :class:`OptimizationAlgorithm`.
 
     This class provides a wrapper for ``cplex.Cplex`` (https://pypi.org/project/cplex/)
     to be used within Qiskit Optimization.
 
     Examples:
+        >>> from qiskit.optimization.problems import QuadraticProgram
+        >>> from qiskit.optimization.algorithms import CplexOptimizer
         >>> problem = QuadraticProgram()
         >>> # specify problem here
         >>> optimizer = CplexOptimizer()
diff --git a/qiskit/optimization/algorithms/grover_optimizer.py b/qiskit/optimization/algorithms/grover_optimizer.py
index 4c95506d28..513f00852c 100644
--- a/qiskit/optimization/algorithms/grover_optimizer.py
+++ b/qiskit/optimization/algorithms/grover_optimizer.py
@@ -22,13 +22,13 @@
 from qiskit import QuantumCircuit
 from qiskit.providers import BaseBackend
 from qiskit.aqua import QuantumInstance
-from qiskit.optimization import QiskitOptimizationError
-from qiskit.optimization.algorithms import OptimizationAlgorithm
-from qiskit.optimization.problems import QuadraticProgram
-from qiskit.optimization.converters import (QuadraticProgramToQubo,
-                                            QuadraticProgramToNegativeValueOracle)
-from qiskit.optimization.algorithms.optimization_algorithm import OptimizationResult
 from qiskit.aqua.algorithms.amplitude_amplifiers.grover import Grover
+from ..exceptions import QiskitOptimizationError
+from .optimization_algorithm import OptimizationAlgorithm, OptimizationResult
+from ..problems.quadratic_program import QuadraticProgram
+from ..converters.quadratic_program_to_qubo import QuadraticProgramToQubo
+from ..converters.quadratic_program_to_negative_value_oracle import \
+    QuadraticProgramToNegativeValueOracle
 
 
 logger = logging.getLogger(__name__)
diff --git a/qiskit/optimization/algorithms/minimum_eigen_optimizer.py b/qiskit/optimization/algorithms/minimum_eigen_optimizer.py
index 4c34a66d21..50f4585142 100644
--- a/qiskit/optimization/algorithms/minimum_eigen_optimizer.py
+++ b/qiskit/optimization/algorithms/minimum_eigen_optimizer.py
@@ -26,7 +26,7 @@
 from ..problems.quadratic_program import QuadraticProgram
 from ..converters.quadratic_program_to_operator import QuadraticProgramToOperator
 from ..converters.quadratic_program_to_qubo import QuadraticProgramToQubo
-from .. import QiskitOptimizationError
+from ..exceptions import QiskitOptimizationError
 
 
 class MinimumEigenOptimizerResult(OptimizationResult):
@@ -67,9 +67,10 @@ def get_correlations(self):
 
 
 class MinimumEigenOptimizer(OptimizationAlgorithm):
-    """A wrapper for minimum eigen solvers from Qiskit Aqua to be used within Qiskit Optimization.
+    """A wrapper for minimum eigen solvers from Qiskit Aqua.
 
-    This class provides a wrapper for minimum eigen solvers from Qiskit Aqua.
+    This class provides a wrapper for minimum eigen solvers from Qiskit Aqua to be used within
+    Qiskit Optimization.
     It assumes a problem consisting only of binary or integer variables as well as linear equality
     constraints thereof. It converts such a problem into a Quadratic Unconstrained Binary
     Optimization (QUBO) problem by expanding integer variables into binary variables and by adding
@@ -80,12 +81,19 @@ class MinimumEigenOptimizer(OptimizationAlgorithm):
     Hamiltonian to find a good solution for the optimization problem.
 
     Examples:
-        >>> problem = QuadraticProgram()
-        >>> # specify problem here
-        >>> # specify minimum eigen solver to be used, e.g., QAOA
-        >>> qaoa = QAOA(...)
-        >>> optimizer = MinEigenOptimizer(qaoa)
-        >>> result = optimizer.solve(problem)
+        Outline of how to use this class:
+
+    .. code-block::
+
+        from qiskit.aqua.algorithms import QAOA
+        from qiskit.optimization.problems import QuadraticProgram
+        from qiskit.optimization.algorithms import MinimumEigenOptimizer
+        problem = QuadraticProgram()
+        # specify problem here
+        # specify minimum eigen solver to be used, e.g., QAOA
+        qaoa = QAOA(...)
+        optimizer = MinimumEigenOptimizer(qaoa)
+        result = optimizer.solve(problem)
     """
 
     def __init__(self, min_eigen_solver: MinimumEigensolver, penalty: Optional[float] = None
diff --git a/qiskit/optimization/algorithms/recursive_minimum_eigen_optimizer.py b/qiskit/optimization/algorithms/recursive_minimum_eigen_optimizer.py
index ec6bdd745e..a6aa05d01f 100644
--- a/qiskit/optimization/algorithms/recursive_minimum_eigen_optimizer.py
+++ b/qiskit/optimization/algorithms/recursive_minimum_eigen_optimizer.py
@@ -39,12 +39,19 @@ class RecursiveMinimumEigenOptimizer(OptimizationAlgorithm):
     The algorithm is introduced in [1].
 
     Examples:
-        >>> problem = QuadraticProgram()
-        >>> # specify problem here
-        >>> # specify minimum eigen solver to be used, e.g., QAOA
-        >>> qaoa = QAOA(...)
-        >>> optimizer = RecursiveMinEigenOptimizer(qaoa)
-        >>> result = optimizer.solve(problem)
+        Outline of how to use this class:
+
+    .. code-block::
+
+        from qiskit.aqua.algorithms import QAOA
+        from qiskit.optimization.problems import QuadraticProgram
+        from qiskit.optimization.algorithms import RecursiveMinimumEigenOptimizer
+        problem = QuadraticProgram()
+        # specify problem here
+        # specify minimum eigen solver to be used, e.g., QAOA
+        qaoa = QAOA(...)
+        optimizer = RecursiveMinimumEigenOptimizer(qaoa)
+        result = optimizer.solve(problem)
 
     References:
         [1]: Bravyi et al. (2019), Obstacles to State Preparation and Variational Optimization
diff --git a/qiskit/optimization/applications/__init__.py b/qiskit/optimization/applications/__init__.py
index 4317685c28..ef32bbdbe7 100644
--- a/qiskit/optimization/applications/__init__.py
+++ b/qiskit/optimization/applications/__init__.py
@@ -11,3 +11,22 @@
 # Any modifications or derivative works of this code must retain this
 # copyright notice, and modified files need to carry a notice indicating
 # that they have been altered from the originals.
+
+"""
+Optimization applications (:mod:`qiskit.aqua.applications`)
+===========================================================
+
+.. currentmodule:: qiskit.optimization.applications
+
+Applications for Qiskit Optimization. The present set are in the form of
+Ising Hamiltonians.
+
+Submodules
+==========
+
+.. autosummary::
+   :toctree:
+
+   ising
+
+"""
diff --git a/qiskit/optimization/applications/ising/__init__.py b/qiskit/optimization/applications/ising/__init__.py
index b9869755a3..f13251435f 100644
--- a/qiskit/optimization/applications/ising/__init__.py
+++ b/qiskit/optimization/applications/ising/__init__.py
@@ -15,7 +15,7 @@
 """
 Ising Models (:mod:`qiskit.optimization.applications.ising`)
 ============================================================
-Ising models for optimization problems
+Ising models for optimization application problems
 
 .. currentmodule:: qiskit.optimization.applications.ising
 
diff --git a/qiskit/optimization/converters/__init__.py b/qiskit/optimization/converters/__init__.py
index 9d41d9c344..06688257e7 100644
--- a/qiskit/optimization/converters/__init__.py
+++ b/qiskit/optimization/converters/__init__.py
@@ -13,26 +13,28 @@
 # that they have been altered from the originals.
 
 """
-===================================================================
-Optimization stack for Aqua (:mod:`qiskit.optimization.converters`)
-===================================================================
+Optimization converters (:mod:`qiskit.optimization.converters`)
+===============================================================
 
 .. currentmodule:: qiskit.optimization.converters
 
-Structures for converting optimization problems
-===============================================
+This is selection of converters having encode, decode functionality to go between different
+forms.
+
+Converters
+==========
 
 .. autosummary::
    :toctree: ../stubs/
    :nosignatures:
 
-    InequalityToEquality
-    IntegerToBinary
-    QuadraticProgramToNegativeValueOracle
-    QuadraticProgramToOperator
-    QuadraticProgramToQubo
-    LinearEqualityToPenalty
-    OperatorToQuadraticProgram
+   InequalityToEquality
+   IntegerToBinary
+   QuadraticProgramToNegativeValueOracle
+   QuadraticProgramToOperator
+   QuadraticProgramToQubo
+   LinearEqualityToPenalty
+   OperatorToQuadraticProgram
 
 """
 
diff --git a/qiskit/optimization/converters/inequality_to_equality.py b/qiskit/optimization/converters/inequality_to_equality.py
index 48d0064f58..b4c8c78bd6 100644
--- a/qiskit/optimization/converters/inequality_to_equality.py
+++ b/qiskit/optimization/converters/inequality_to_equality.py
@@ -18,6 +18,7 @@
 from typing import List, Tuple, Dict, Optional
 import logging
 
+from ..algorithms.optimization_algorithm import OptimizationResult
 from ..problems.quadratic_program import QuadraticProgram
 from ..problems.quadratic_objective import QuadraticObjective
 from ..problems.constraint import Constraint
@@ -31,6 +32,8 @@ class InequalityToEquality:
     """Convert inequality constraints into equality constraints by introducing slack variables.
 
     Examples:
+        >>> from qiskit.optimization.problems import QuadraticProgram
+        >>> from qiskit.optimization.converters import InequalityToEquality
         >>> problem = QuadraticProgram()
         >>> # define a problem
         >>> conv = InequalityToEquality()
@@ -54,10 +57,11 @@ def encode(
             op: The problem to be solved, that may contain inequality constraints.
             name: The name of the converted problem.
             mode: To chose the type of slack variables. There are 3 options for mode.
-                  - 'integer': All slack variables will be integer variables.
-                  - 'continuous': All slack variables will be continuous variables
-                  - 'auto': Try to use integer variables but if it's not possible,
-                    use continuous variables
+
+                - 'integer': All slack variables will be integer variables.
+                - 'continuous': All slack variables will be continuous variables
+                - 'auto': Try to use integer variables but if it's not possible,
+                   use continuous variables
 
         Returns:
             The converted problem, that contain only equality constraints.
@@ -332,7 +336,7 @@ def _calc_quadratic_bounds(self, linear, quadratic):
             )
         return lhs_lb, lhs_ub
 
-    def decode(self, result: 'OptimizationResult') -> 'OptimizationResult':
+    def decode(self, result: OptimizationResult) -> OptimizationResult:
         """Convert a result of a converted problem into that of the original problem.
 
         Args:
diff --git a/qiskit/optimization/converters/integer_to_binary.py b/qiskit/optimization/converters/integer_to_binary.py
index f09051b147..f4f148b008 100644
--- a/qiskit/optimization/converters/integer_to_binary.py
+++ b/qiskit/optimization/converters/integer_to_binary.py
@@ -20,6 +20,7 @@
 
 import numpy as np
 
+from ..algorithms.optimization_algorithm import OptimizationResult
 from ..exceptions import QiskitOptimizationError
 from ..problems.quadratic_objective import QuadraticObjective
 from ..problems.quadratic_program import QuadraticProgram
@@ -29,13 +30,16 @@
 
 
 class IntegerToBinary:
-    """Convert an `QuadraticProgram` into new one by encoding integer with binary variables.
+    """Convert a :class:`~qiskit.optimization.problems.QuadraticProgram` into new one by encoding
+    integer with binary variables.
 
     This bounded-coefficient encoding used in this converted is proposed in [1], Eq. (5).
 
     Examples:
+        >>> from qiskit.optimization.problems import QuadraticProgram
+        >>> from qiskit.optimization.converters import IntegerToBinary
         >>> problem = QuadraticProgram()
-        >>> problem.integer_var(name='x', lowerbound=0, upperbound=10)
+        >>> var = problem.integer_var(name='x', lowerbound=0, upperbound=10)
         >>> conv = IntegerToBinary()
         >>> problem2 = conv.encode(problem)
 
@@ -202,7 +206,7 @@ def _substitute_int_var(self):
             self._dst.quadratic_constraint(linear, quadratic, constraint.sense,
                                            constraint.rhs - constant, constraint.name)
 
-    def decode(self, result: "OptimizationResult") -> "OptimizationResult":
+    def decode(self, result: OptimizationResult) -> OptimizationResult:
         """Convert the encoded problem (binary variables) back to the original (integer variables).
 
         Args:
diff --git a/qiskit/optimization/converters/linear_equality_to_penalty.py b/qiskit/optimization/converters/linear_equality_to_penalty.py
index e87f84a664..5526169859 100644
--- a/qiskit/optimization/converters/linear_equality_to_penalty.py
+++ b/qiskit/optimization/converters/linear_equality_to_penalty.py
@@ -17,7 +17,10 @@
 import copy
 from typing import Optional
 
-from ..problems import QuadraticProgram, Variable, Constraint, QuadraticObjective
+from ..problems.quadratic_program import QuadraticProgram
+from ..problems.variable import Variable
+from ..problems.constraint import Constraint
+from ..problems.quadratic_objective import QuadraticObjective
 from ..exceptions import QiskitOptimizationError
 
 
diff --git a/qiskit/optimization/converters/operator_to_quadratic_program.py b/qiskit/optimization/converters/operator_to_quadratic_program.py
index e808ff6ccc..edc35e1a12 100644
--- a/qiskit/optimization/converters/operator_to_quadratic_program.py
+++ b/qiskit/optimization/converters/operator_to_quadratic_program.py
@@ -19,7 +19,7 @@
 
 import numpy as np
 
-from qiskit.aqua.operators import WeightedPauliOperator
+from qiskit.aqua.operators.legacy import WeightedPauliOperator
 from ..problems.quadratic_program import QuadraticProgram
 from ..exceptions import QiskitOptimizationError
 
@@ -39,11 +39,12 @@ def encode(self, qubit_op: WeightedPauliOperator, offset: float = 0.0) -> Quadra
         """Convert a qubit operator and a shift value into a quadratic program
 
         Args:
-            qubit_op: The qubit operator to be converted into `QuadraticProgram`
+            qubit_op: The qubit operator to be converted into a
+                :class:`~qiskit.optimization.problems.quadratic_program.QuadraticProgram`
             offset: The shift value of the qubit operator
 
         Returns:
-            QuadraticProgram: converted from the input qubit operator and the shift value
+            QuadraticProgram converted from the input qubit operator and the shift value
 
         Raises:
             QiskitOptimizationError: If there are Pauli Xs in any Pauli term
diff --git a/qiskit/optimization/converters/quadratic_program_to_negative_value_oracle.py b/qiskit/optimization/converters/quadratic_program_to_negative_value_oracle.py
index 0d4ade34f4..4007452dcf 100644
--- a/qiskit/optimization/converters/quadratic_program_to_negative_value_oracle.py
+++ b/qiskit/optimization/converters/quadratic_program_to_negative_value_oracle.py
@@ -23,7 +23,7 @@
 from qiskit.circuit.library import QFT
 from qiskit.aqua.components.initial_states import Custom
 from qiskit.aqua.components.oracles import CustomCircuitOracle
-from qiskit.optimization.problems import QuadraticProgram
+from ..problems.quadratic_program import QuadraticProgram
 
 logger = logging.getLogger(__name__)
 
diff --git a/qiskit/optimization/converters/quadratic_program_to_qubo.py b/qiskit/optimization/converters/quadratic_program_to_qubo.py
index 5e9e15b04e..e7abbd158e 100644
--- a/qiskit/optimization/converters/quadratic_program_to_qubo.py
+++ b/qiskit/optimization/converters/quadratic_program_to_qubo.py
@@ -16,17 +16,19 @@
 
 from typing import Optional
 
-from qiskit.optimization.problems import QuadraticProgram
-from qiskit.optimization.problems.constraint import Constraint
-from qiskit.optimization.converters.linear_equality_to_penalty import LinearEqualityToPenalty
-from qiskit.optimization.converters.integer_to_binary import IntegerToBinary
-from qiskit.optimization.exceptions import QiskitOptimizationError
+from ..algorithms.optimization_algorithm import OptimizationResult
+from ..problems.quadratic_program import QuadraticProgram
+from ..problems.constraint import Constraint
+from ..converters.linear_equality_to_penalty import LinearEqualityToPenalty
+from ..exceptions import QiskitOptimizationError
 
 
 class QuadraticProgramToQubo:
     """Convert a given optimization problem to a new problem that is a QUBO.
 
         Examples:
+            >>> from qiskit.optimization.problems import QuadraticProgram
+            >>> from qiskit.optimization.converters import QuadraticProgramToQubo
             >>> problem = QuadraticProgram()
             >>> # define a problem
             >>> conv = QuadraticProgramToQubo()
@@ -38,6 +40,7 @@ def __init__(self, penalty: Optional[float] = None) -> None:
         Args:
             penalty: Penalty factor to scale equality constraints that are added to objective.
         """
+        from ..converters.integer_to_binary import IntegerToBinary
         self._int_to_bin = IntegerToBinary()
         self._penalize_lin_eq_constraints = LinearEqualityToPenalty()
         self._penalty = penalty
@@ -74,7 +77,7 @@ def encode(self, problem: QuadraticProgram) -> QuadraticProgram:
         # return QUBO
         return problem_
 
-    def decode(self, result: 'OptimizationResult') -> 'OptimizationResult':
+    def decode(self, result: OptimizationResult) -> OptimizationResult:
         """ Convert a result of a converted problem into that of the original problem.
 
             Args:
diff --git a/qiskit/optimization/exceptions.py b/qiskit/optimization/exceptions.py
index aa14a50fed..71baf4ca19 100644
--- a/qiskit/optimization/exceptions.py
+++ b/qiskit/optimization/exceptions.py
@@ -18,5 +18,5 @@
 
 
 class QiskitOptimizationError(AquaError):
-    """Class for errors returned by Qiskit Optimization libraries functions."""
+    """Class for errors returned by Qiskit Optimization."""
     pass
diff --git a/qiskit/optimization/problems/__init__.py b/qiskit/optimization/problems/__init__.py
index f0b0495df1..c5e7c8e397 100644
--- a/qiskit/optimization/problems/__init__.py
+++ b/qiskit/optimization/problems/__init__.py
@@ -13,14 +13,24 @@
 # that they have been altered from the originals.
 
 """
-=================================================================
-Optimization stack for Aqua (:mod:`qiskit.optimization.problems`)
-=================================================================
+Optimization problems (:mod:`qiskit.optimization.problems`)
+===========================================================
 
 .. currentmodule:: qiskit.optimization.problems
 
-Structures for defining an optimization problem and its solution
-================================================================
+Problems
+========
+Structures for defining an optimization problem and its solution.
+
+.. autosummary::
+   :toctree: ../stubs/
+   :nosignatures:
+
+   QuadraticProgram
+
+Note:
+    The following classes are not intended to be instantiated directly.
+    Objects of these types are available within an instantiated :class:`QuadraticProgram`.
 
 .. autosummary::
    :toctree: ../stubs/
@@ -32,12 +42,8 @@
    QuadraticExpression
    QuadraticConstraint
    QuadraticObjective
-   QuadraticProgram
    Variable
 
-N.B. All classes but `QuadraticProgram` are not to be instantiated directly.
-Objects of those types are available within an instantiated `QuadraticProgram`.
-
 """
 
 from .constraint import Constraint
diff --git a/qiskit/optimization/problems/constraint.py b/qiskit/optimization/problems/constraint.py
index fa7390beb8..36ae94feb6 100644
--- a/qiskit/optimization/problems/constraint.py
+++ b/qiskit/optimization/problems/constraint.py
@@ -16,7 +16,7 @@
 
 from abc import abstractmethod
 from enum import Enum
-from typing import Union, List, Dict
+from typing import Union, List, Dict, Any
 
 from numpy import ndarray
 
@@ -63,7 +63,7 @@ class Constraint(QuadraticProgramElement):
 
     Sense = ConstraintSense
 
-    def __init__(self, quadratic_program: 'QuadraticProgram', name: str, sense: ConstraintSense,
+    def __init__(self, quadratic_program: Any, name: str, sense: ConstraintSense,
                  rhs: float) -> None:
         """ Initializes the constraint.
 
diff --git a/qiskit/optimization/problems/linear_constraint.py b/qiskit/optimization/problems/linear_constraint.py
index 467d30f952..6b55abaff0 100644
--- a/qiskit/optimization/problems/linear_constraint.py
+++ b/qiskit/optimization/problems/linear_constraint.py
@@ -14,20 +14,23 @@
 
 """Linear Constraint."""
 
-from typing import Union, List, Dict
+from typing import Union, List, Dict, Any
 
 from numpy import ndarray
 from scipy.sparse import spmatrix
 
-from qiskit.optimization.problems.constraint import Constraint
-from qiskit.optimization.problems.linear_expression import LinearExpression
+from .constraint import Constraint, ConstraintSense
+from .linear_expression import LinearExpression
 
 
 class LinearConstraint(Constraint):
     """ Representation of a linear constraint."""
 
+    # Note: added, duplicating in effect that in Constraint, to avoid issues with Sphinx
+    Sense = ConstraintSense
+
     def __init__(self,
-                 quadratic_program: "QuadraticProgram", name: str,
+                 quadratic_program: Any, name: str,
                  linear: Union[ndarray, spmatrix, List[float], Dict[Union[str, int], float]],
                  sense: Constraint.Sense,
                  rhs: float
diff --git a/qiskit/optimization/problems/linear_expression.py b/qiskit/optimization/problems/linear_expression.py
index 945aacbdb5..03d0e7f2a2 100644
--- a/qiskit/optimization/problems/linear_expression.py
+++ b/qiskit/optimization/problems/linear_expression.py
@@ -14,19 +14,19 @@
 
 """Linear expression interface."""
 
-from typing import List, Union, Dict
+from typing import List, Union, Dict, Any
 
 from numpy import ndarray
 from scipy.sparse import spmatrix, dok_matrix
 
-from qiskit.optimization import QiskitOptimizationError
-from qiskit.optimization.problems.quadratic_program_element import QuadraticProgramElement
+from .quadratic_program_element import QuadraticProgramElement
+from ..exceptions import QiskitOptimizationError
 
 
 class LinearExpression(QuadraticProgramElement):
     """ Representation of a linear expression by its coefficients."""
 
-    def __init__(self, quadratic_program: "QuadraticProgram",
+    def __init__(self, quadratic_program: Any,
                  coefficients: Union[ndarray, spmatrix, List[float],
                                      Dict[Union[int, str], float]]) -> None:
         """Creates a new linear expression.
diff --git a/qiskit/optimization/problems/quadratic_constraint.py b/qiskit/optimization/problems/quadratic_constraint.py
index f87cbab6ba..a4078e485a 100644
--- a/qiskit/optimization/problems/quadratic_constraint.py
+++ b/qiskit/optimization/problems/quadratic_constraint.py
@@ -14,21 +14,24 @@
 
 """Quadratic Constraint."""
 
-from typing import Union, List, Dict, Tuple
+from typing import Union, List, Dict, Tuple, Any
 
 from numpy import ndarray
 from scipy.sparse import spmatrix
 
-from qiskit.optimization.problems.constraint import Constraint
-from qiskit.optimization.problems.linear_expression import LinearExpression
-from qiskit.optimization.problems.quadratic_expression import QuadraticExpression
+from .constraint import Constraint, ConstraintSense
+from .linear_expression import LinearExpression
+from .quadratic_expression import QuadraticExpression
 
 
 class QuadraticConstraint(Constraint):
     """ Representation of a quadratic constraint."""
 
+    # Note: added, duplicating in effect that in Constraint, to avoid issues with Sphinx
+    Sense = ConstraintSense
+
     def __init__(self,
-                 quadratic_program: "QuadraticProgram", name: str,
+                 quadratic_program: Any, name: str,
                  linear: Union[ndarray, spmatrix, List[float], Dict[Union[str, int], float]],
                  quadratic: Union[ndarray, spmatrix, List[List[float]],
                                   Dict[Tuple[Union[int, str], Union[int, str]], float]],
diff --git a/qiskit/optimization/problems/quadratic_expression.py b/qiskit/optimization/problems/quadratic_expression.py
index d219f1f6b4..43555e0af9 100644
--- a/qiskit/optimization/problems/quadratic_expression.py
+++ b/qiskit/optimization/problems/quadratic_expression.py
@@ -14,20 +14,20 @@
 
 """Quadratic expression interface."""
 
-from typing import List, Union, Dict, Tuple
+from typing import List, Union, Dict, Tuple, Any
 
 import numpy as np
 from numpy import ndarray
 from scipy.sparse import spmatrix, dok_matrix, tril, triu
 
-from qiskit.optimization import QiskitOptimizationError
-from qiskit.optimization.problems.quadratic_program_element import QuadraticProgramElement
+from .quadratic_program_element import QuadraticProgramElement
+from ..exceptions import QiskitOptimizationError
 
 
 class QuadraticExpression(QuadraticProgramElement):
     """ Representation of a quadratic expression by its coefficients."""
 
-    def __init__(self, quadratic_program: "QuadraticProgram",
+    def __init__(self, quadratic_program: Any,
                  coefficients: Union[ndarray, spmatrix, List[List[float]],
                                      Dict[Tuple[Union[int, str], Union[int, str]], float]]) -> None:
         """Creates a new quadratic expression.
diff --git a/qiskit/optimization/problems/quadratic_objective.py b/qiskit/optimization/problems/quadratic_objective.py
index 7d2f9f32fd..82b16e192b 100644
--- a/qiskit/optimization/problems/quadratic_objective.py
+++ b/qiskit/optimization/problems/quadratic_objective.py
@@ -15,14 +15,14 @@
 """Quadratic Objective."""
 
 from enum import Enum
-from typing import Union, List, Dict, Tuple
+from typing import Union, List, Dict, Tuple, Any
 
 from numpy import ndarray
 from scipy.sparse import spmatrix
 
-from qiskit.optimization.problems.quadratic_program_element import QuadraticProgramElement
-from qiskit.optimization.problems.linear_constraint import LinearExpression
-from qiskit.optimization.problems.quadratic_expression import QuadraticExpression
+from .linear_constraint import LinearExpression
+from .quadratic_expression import QuadraticExpression
+from .quadratic_program_element import QuadraticProgramElement
 
 
 class ObjSense(Enum):
@@ -38,7 +38,7 @@ class QuadraticObjective(QuadraticProgramElement):
 
     Sense = ObjSense
 
-    def __init__(self, quadratic_program: "QuadraticProgram",
+    def __init__(self, quadratic_program: Any,
                  constant: float = 0.0,
                  linear: Union[ndarray, spmatrix, List[float], Dict[Union[str, int], float]] = None,
                  quadratic: Union[ndarray, spmatrix, List[List[float]],
diff --git a/qiskit/optimization/problems/quadratic_program.py b/qiskit/optimization/problems/quadratic_program.py
index 90c0109124..d8ce685f45 100644
--- a/qiskit/optimization/problems/quadratic_program.py
+++ b/qiskit/optimization/problems/quadratic_program.py
@@ -29,14 +29,15 @@
 from numpy import ndarray
 from scipy.sparse import spmatrix
 
-from qiskit.optimization import INFINITY, QiskitOptimizationError
-from qiskit.optimization.problems.constraint import Constraint
-from qiskit.optimization.problems.linear_constraint import LinearConstraint
-from qiskit.optimization.problems.linear_expression import LinearExpression
-from qiskit.optimization.problems.quadratic_constraint import QuadraticConstraint
-from qiskit.optimization.problems.quadratic_expression import QuadraticExpression
-from qiskit.optimization.problems.quadratic_objective import QuadraticObjective
-from qiskit.optimization.problems.variable import Variable
+from .constraint import Constraint
+from .linear_constraint import LinearConstraint
+from .linear_expression import LinearExpression
+from .quadratic_constraint import QuadraticConstraint
+from .quadratic_expression import QuadraticExpression
+from .quadratic_objective import QuadraticObjective
+from .variable import Variable
+from ..exceptions import QiskitOptimizationError
+from ..infinity import INFINITY
 
 logger = logging.getLogger(__name__)
 
@@ -48,15 +49,15 @@ class QuadraticProgramStatus(Enum):
 
 
 class QuadraticProgram:
-    """Representation of a Quadratically Constrained Quadratic Program supporting inequality and
-    equality constraints as well as continuous, binary, and integer variables.
-    """
+    """Quadratically Constrained Quadratic Program representation.
 
+    This representation supports inequality and equality constraints,
+    as well as continuous, binary, and integer variables.
+    """
     Status = QuadraticProgramStatus
 
     def __init__(self, name: str = '') -> None:
-        """Constructs a quadratic program.
-
+        """
         Args:
             name: The name of the quadratic program.
         """
diff --git a/qiskit/optimization/problems/quadratic_program_element.py b/qiskit/optimization/problems/quadratic_program_element.py
index f17bea036a..662475e549 100644
--- a/qiskit/optimization/problems/quadratic_program_element.py
+++ b/qiskit/optimization/problems/quadratic_program_element.py
@@ -14,20 +14,29 @@
 
 """Interface for all objects that have a parent QuadraticProgram."""
 
+from typing import Any
+
 
 class QuadraticProgramElement:
     """Interface class for all objects that have a parent QuadraticProgram."""
 
-    def __init__(self, quadratic_program: "QuadraticProgram") -> None:
+    def __init__(self, quadratic_program: Any) -> None:
         """ Initialize object with parent QuadraticProgram.
 
         Args:
             quadratic_program: The parent QuadraticProgram.
+        Raises:
+            TypeError: QuadraticProgram instance expected.
         """
+        from .quadratic_program import QuadraticProgram
+
+        if not isinstance(quadratic_program, QuadraticProgram):
+            raise TypeError('QuadraticProgram instance expected')
+
         self._quadratic_program = quadratic_program
 
     @property
-    def quadratic_program(self) -> "QuadraticProgram":
+    def quadratic_program(self) -> Any:
         """Returns the parent QuadraticProgram.
 
         Returns:
@@ -36,10 +45,18 @@ def quadratic_program(self) -> "QuadraticProgram":
         return self._quadratic_program
 
     @quadratic_program.setter
-    def quadratic_program(self, quadratic_program: "QuadraticProgram") -> None:
+    def quadratic_program(self, quadratic_program: Any) -> None:
         """Sets the parent QuadraticProgram.
 
         Args:
             quadratic_program: The parent QuadraticProgram.
+        Raises:
+            TypeError: QuadraticProgram instance expected.
         """
+        # pylint: disable=cyclic-import
+        from .quadratic_program import QuadraticProgram
+
+        if not isinstance(quadratic_program, QuadraticProgram):
+            raise TypeError('QuadraticProgram instance expected')
+
         self._quadratic_program = quadratic_program
diff --git a/qiskit/optimization/problems/variable.py b/qiskit/optimization/problems/variable.py
index 97cd8e685b..f1516f10d6 100644
--- a/qiskit/optimization/problems/variable.py
+++ b/qiskit/optimization/problems/variable.py
@@ -15,10 +15,11 @@
 """Variable interface"""
 
 from enum import Enum
-from typing import Tuple, Union
+from typing import Tuple, Union, Any
 
-from qiskit.optimization import INFINITY, QiskitOptimizationError
-from qiskit.optimization.problems.quadratic_program_element import QuadraticProgramElement
+from .quadratic_program_element import QuadraticProgramElement
+from ..exceptions import QiskitOptimizationError
+from ..infinity import INFINITY
 
 
 class VarType(Enum):
@@ -33,7 +34,7 @@ class Variable(QuadraticProgramElement):
 
     Type = VarType
 
-    def __init__(self, quadratic_program: 'QuadraticProgram', name: str,
+    def __init__(self, quadratic_program: Any, name: str,
                  lowerbound: Union[float, int] = 0,
                  upperbound: Union[float, int] = INFINITY,
                  vartype: VarType = VarType.CONTINUOUS) -> None: