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

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.