新的拉格朗日乘子方法

New Lagrangian Multiplier Methods

摘要:

对于约束优化问题,提出一类新的结合 FischerBurmeister 非线性互补(NCP)函数的增广拉格朗日函数,它的无约束极小解对应于原约束问题(NLP)的解及其乘子; 同时提出相对应的拉格朗日乘子方法.该方法可实现并具有全局收敛性.

关键词:约束优化; 非线性互补函数; 拉格朗日函数; 乘子; 收敛性

Abstract:

A new class of augmented Lagrangian functions with the FischerBurmeister NCP function and a Lagrangian multiplier method are proposed for the minimization of a smooth function subject to smooth equation and inequality constraints.This method is based on the solutions of the unconstrained optimization which is a reformulation of the primal constrained problem.These methods are implementable and globally convergent.

Key words:constrained optimization; nonlinear complementarity function; Lagrangian function; multiplier; convergence