求解约束规划的一个非线性Lagrange函数  

A Nonlinear Lagrangian for Constrained Programming

作　　者：顾剑 任咏红[1] 

机构地区：[1]大连理工大学应用数学系,大连辽宁116024

出　　处：《数学进展》2007年第6期749-760,共12页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10471015).

摘　　要：本文提出了一个求解不等式约束优化问题的非线性Lagrange函数,并构造了基于该函数的对偶算法.证明了当参数σ小于某一阈值σ_0时,由算法生成的原始-对偶点列是局部收敛的,并给出了原始-对偶解的误差估计.此外,建立了基于该函数的对偶理论.最后给出了算法的数值结果.This paper establishes a nonlinear Lagrangian for solving nonlinear programming problems with inequality constraints. We prove that there exists a threshold such that the sequence of primal-dual iterate points generated by dual algorithm basing on the nonlinear Lagrangian locally converges to a minimizer if the penalty parameter is lower than the threshold. We also give the error bound of pimal-dual solutions. Moreover, we develop corresponding duality theory. Finally we report some numerical results by using the proposed dual algorithm.

关 键 词：非线性LAGRANGE函数 对偶算法 对偶函数 鞍点 

分 类 号：O157.5[理学—数学]