基于修正的Carroll函数的概率约束优化问题的对偶算法

A Dual Algorithm for Probabilistic Constrained Optimization Problems Based on Modified Carroll Functions

摘要: 本文用连续可微非凸函数描述的概率约束分析非线性随机优化问题。为此描述了潜在概率函数的水平集的切锥和法锥，并在此基础上，提出p-有效点的定义，形成问题的一阶和二阶最优性条件，基于p-有效点生成的概率函数的水平集，通过修正的Carroll函数生成一个对偶算法。

Abstract: In this paper, probabilistic constraints described by continuously differentiable non-convex functions are used to analyze nonlinear stochastic optimization problems. To this end, the tangent and normal cones of the level set of potential probability functions are described, and on this basis, the definition of p-effective points is proposed to form the first and second order optimality conditions of the problem. Based on the water-level set of probability functions generated by p-effective points, a dual algorithm is generated by the modified Carroll function.