求解约束规划的一个非线性Lagrange函数

A Nonlinear Lagrangian for Constrained Programming

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.