基于修正的Frish函数的求解概率约束优化问题的对偶算法  

A dual algorithm for probabilistic constrained optimization problems based on modified Frish function

作　　者：任咏红[1] 冯千千 邵鑫宇 REN Yonghong;FENG Qianqian;SHAO Xinyu(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报(自然科学版)》2025年第1期68-73,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省属本科高校基本科研业务费专项基金资助项目(LS2024L001)。

摘　　要：考虑具有概率约束的随机优化问题,该类问题在风险评估及优化等许多领域中具有重要的应用价值.基于随机变量的概率分布的p-有效点和水平集的概念,将概率约束优化问题(PCOP)转化为锥约束优化问题(CCOP).进而,给出了相应的最优性条件,并构建了近似的非线性优化问题(NLP).构造了基于修正的Frish函数的非线性Lagrange函数,设计了求解问题(PCOP)的对偶算法.在满足一系列特定条件的前提下,论证了该对偶算法产生的点列的聚点满足一阶必要条件.Consider stochastic optimization problems with probabilistic constraints,which have significant application value in many fields such as risk assessment and optimization,etc.Based on the concepts of p-efficient points and level sets of the probability distribution of random variables,the probabilistic constrained optimization problem(PCOP)is transformed into a cone-constrained optimization problem(CCOP).Furthermore,corresponding optimality conditions are provided,and an approximation nonlinear optimization problem(NLP)is constructed.A nonlinear Lagrange function based on the modified Frish function is constructed,and a dual algorithm for solving the problem(PCOP)is designed.Under a series of specific conditions,it is demonstrated that the accumulation points of the sequence of points generated by the dual algorithm satisfy the first-order necessary conditions.

关 键 词：概率约束 p-有效点 修正的Frish函数 对偶算法 

分 类 号：O221.5[理学—运筹学与控制论]