求解半无限规划问题的一个非线性Lagrange函数  

A nonlinear Lagrangian for solving semi-infinite programming problem

作　　者：任咏红[1] 李英芝[1] 张丽丽[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2010年第4期407-412,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省博士科研启动基金项目(20091046);辽宁省教育厅科学技术研究项目(2008376)

摘　　要：由于工程、经济等领域的许多实际问题数学模型均为半无限规划问题,近年来,半无限规划问题成为求解实际问题的强有力工具.旨在探讨用于求解半无限规划问题的非线性Lagrange函数.在一定的条件下,将半无限规划问题转化为有限的离散化问题,并提出相应的非线性Lagrange乘子存在的充分必要条件.最后,给出了具体算例说明非线性Lagrange乘子的存在性.There are many applications from engineering and economics which can be modeled as a semi-infinite programming（SIP） problem.In recent years,SIP problems has become a powerful tool for the mathematical modeling of many real-life problems.This article aims at discussing a nonlinear Lagrangian for solving semi-infinite programming problem.Under certain conditions,the SIP problem can be transformed into a discretization problem with a finite number of smooth constraints.The necessary and sufficient conditions for the existence of corresponding nonlinear Lagrange multiplier are presented.Finally,we show an illustrating example about existence of nonlinear Lagrange multiplier.

关 键 词：半无限规划 非线性Lagrange乘子 非线性LAGRANGE函数 对偶 鞍点 

分 类 号：O221.2[理学—运筹学与控制论]