A 0/1 Constrained Optimization Solving Sample Average Approximation for Chance Constrained Programming

• 成果类型: Article; Early Access
• 署名作者: Zhou, Shenglong; Pan, Lili; Xiu, Naihua; Li, Geoffrey Ye
• 署名单位: Beijing Jiaotong University; Imperial College London
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0149
• 发表日期: 2024
• 关键词: probability functions; convex approximations; gradient formulas; newton; regularization; CONVERGENCE; management; algorithm; networks; systems

摘要

Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the 0/1 loss function, which results in considerable complexities in devising numerical algorithms. Most existing methods have been devised based on reformulations of SAA, such as binary integer programming or relaxed problems. However, the development of viable methods to directly tackle SAA remains elusive, let alone providing theoretical guarantees. In this paper, we investigate a general 0/1 constrained optimization, providing a new way to address SAA rather than its reformulations. Specifically, starting with deriving the Bouligand tangent and Frechet normal cones of the 0/1 constraint, we establish several optimality conditions. One of them can be equivalently expressed by a system of equations, enabling the development of a semismooth Newtontype algorithm. The algorithm demonstrates a locally superlinear or quadratic convergence rate under standard assumptions along with nice numerical performance compared with several leading solvers.