Solving Chance Constrained Programs via a Penalty based Difference of Convex Approach

TL;DR

This paper introduces two novel penalty-based difference of convex algorithms for solving chance constrained programs, improving stability and efficiency without requiring feasible initial solutions.

Contribution

The paper proposes new primal and lifted space DC algorithms for chance constrained programs, with guarantees and improved numerical stability.

Findings

Algorithms outperform state-of-the-art benchmarks

Proximal penalty method does not need feasible initialization

Lifted formulation enhances numerical stability

Abstract

We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the primal space that does not require a feasible initialization. Second, to improve numerical stability in the general nonlinear settings, we derive an equivalent lifted formulation with complementary constraints and show that, after minimizing primal variables, the penalized lifted problem admits a tractable DC structure in the dual space over a simple polyhedron. We then develop a penalty based DC algorithm in the lifted space with a finite termination guarantee. We establish exact penalty and stationarity guarantees under mild constraint qualifications and identify the relationship of the local minimizers between the two formulations. Numerical experiments demonstrate the efficiency and effectiveness of our proposed methods compared with state-of-the-art benchmarks.