A STOCHASTIC AUGMENTED LAGRANGIAN METHOD FOR STOCHASTIC CONVEX PROGRAMMING  

作　　者：Jiani Wang Liwei Zhang 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China

出　　处：《Journal of Computational Mathematics》2025年第2期315-344,共30页计算数学(英文)

基　　金：supported by the National Key R&D Program of China(Project No.2022YFA1004000);by the Natural Science Foundation of China(Project No.12371298).

摘　　要：In this paper,we analyze the convergence properties of a stochastic augmented Lagrangian method for solving stochastic convex programming problems with inequality constraints.Approximation models for stochastic convex programming problems are constructed from stochastic observations of real objective and constraint functions.Based on relations between solutions of the primal problem and solutions of the dual problem,it is proved that the convergence of the algorithm from the perspective of the dual problem.Without assumptions on how these random models are generated,when estimates are merely sufficiently accurate to the real objective and constraint functions with high enough,but fixed,probability,the method converges globally to the optimal solution almost surely.In addition,sufficiently accurate random models are given under different noise assumptions.We also report numerical results that show the good performance of the algorithm for different convex programming problems with several random models.

关 键 词：Stochastic convex optimization Stochastic approximation Augmented Lagrangian method Duality theory 

分 类 号：O17[理学—数学]