MPCC问题的PAM稳定性研究  

The PAM-stationarity for mathematical programs with complementarity constraints

作　　者：许娜 宁晶 王子平 XU Na;NING Jing;WANG Ziping(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）》2024年第4期458-464,共7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资金资助项目(LS2024L003)。

摘　　要：带有互补约束的数学规划(MPCC)问题是一类重要的优化问题,在经济学、工程设计、最优控制等领域都有着重要的应用.近年来,非线性规划(NLP)问题的序列最优性条件被广泛关注,但是由于MPCC问题的特殊结构,NLP问题的序列最优性条件往往并不适用于MPCC问题.基于NLP问题的PAKKT条件,提出了一个关于MPCC问题的新的序列最优性条件,即MPCC-PAM稳定性,并证明了在新的约束规范MPCC-PAM正则性下,MPCC-PAM稳定性可以得到MPCC问题的M稳定性.Mathematical programs with complementarity constraints(MPCC)form an important class of optimization problems,which have numerous applications in areas such as economic sciences,engineering design and optimal control.In recent years,sequential optimality conditions have been widely concerned with nonlinear optimization problems.However,due to the particular structure of MPCC,the established sequential optimality conditions are not suitable for MPCC.In this paper,we present a new sequential optimality condition for MPCC derived from the positive approximate KKT condition for nonlinear programming.We refer to these conditions as MPCC-PAM-stationarity.Furthermore,we show that the MPCC-PAM point is M-stationarity under the MPCC-PAM-regular constraint qualification.

关 键 词：带有互补约束的数学规划问题 序列最优性条件 约束规范 

分 类 号：O224[理学—运筹学与控制论]