Approximate Methods for Solving Chance Constrained Linear Programs in Probability Measure Space

TL;DR

This paper introduces the first numerical methods to approximately solve intractable chance-constrained linear programs in probability measure space, with proven convergence and validated through experiments.

Contribution

It proposes two novel approximate optimization problems for chance-constrained linear programs in probability measure space and proves their uniform convergence.

Findings

Proposed methods are numerically validated.

Proven uniform convergence of the approximate problems.

First numerical solutions for this class of problems.

Abstract

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to solve this problem. This paper presents numerical methods to solve chance-constrained linear programs in probability measure space for the first time. We propose two solvable optimization problems as approximate problems of the original problem. We prove the uniform convergence of each approximate problem. Moreover, numerical experiments have been implemented to validate the proposed methods.