非线性规划问题的精确增广Lagrange函数  

Exact Augmented Lagrangian Function for Nonlinear Programming

作　　者：刘水霞[1] 陈国庆[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2011年第19期150-155,共6页Mathematics in Practice and Theory

基　　金：内蒙古自治区"111人才工程"

摘　　要：对于一般的非线性规划给出一种精确增广Lagrange函数,并讨论其性质.无需假设严格互补条件成立,给出了原问题的局部极小点与增广Lagrange函数在原问题的变量空间上的局部极小的关系.进一步,在适当的假设条件下,建立了两者的全局最优解之间的关系.An exact augmented Lagrangian function for the nonlinear programming problems with equality constraints and inequality constraints is provided, and its properties is discussed. Without requiring strict complementarity condition, the relationship was es- tablished between the local of the original constrained problem and the local unconstrained minimizers of the augmented Lagrangian function on the space of the origined problem variables. Furthermore, under some assumptions, the relationship of the global solutions was established between the augmented Lagrangian function and the original constrained problem.

关 键 词：增广LAGRANGE函数 严格互补条件 全局最优解 

分 类 号：O221.2[理学—运筹学与控制论]