Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach

Introduction

This is a Matlab implementation of the sequential convex approximation algorithms for joint chance constrained problem. It includes a comparison between both conditional value-at-risk (CVaR) and sequential convex approximation for value-at-risk (Iterative dc).

Using the code

Use Matlab to run example_run.m directly. You may expect to see the result figure below:

Files explanation:

• example_run.m: runing file, first open
• main_function.m: including generating samples, apply cvar approximation, epsilon approximation and dc approximation, return results for a particular setting
• gensample.m: generate normal distributions for all random variables
• obj_fun.m: objective function
• quantile.m: quantile for constraints
• opt_cvar.m, opt_dc.m, opt_eps.m: optimization for cvar, one step dc approximation, epsilon approximation
• con_fun_cvar.m, con_fun_dc.m, con_fun_eps.m: constraints for cvar, one step dc approximation, epsilon approximation
• lincave.m: linear approximation for concave function

Citation

@article{hong2011sequential,
  title={Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach},
  author={Hong, L Jeff and Yang, Yi and Zhang, Liwei},
  journal={Operations Research},
  volume={59},
  number={3},
  pages={617--630},
  year={2011},
  publisher={INFORMS}
}