拟可微约束优化的次线性Lagrange乘子法则  

Sublinear Lagrange Rules for Quasidifferentiable Programming

作　　者：宋春玲[1] 夏尊铨[2] 谢琳[3] 

机构地区：[1]佛山科学技术学院理学院,广东佛山528000 [2]大连理工大学应用数学系,辽宁大连116024 [3]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2006年第2期153-155,共3页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家博士点基金资助项目(20020141013);国家自然科学基金资助项目(10001007)

摘　　要：约束拟可微优化的Lagrange乘子型最优性条件,往往与某些特殊对象(超梯度,方向)的选取有关,这是拟可微优化的核心问题之一.应用凸紧集与次线性函数的Minkowski对偶,利用次线性泛函产生的非线性Lagrange函数,对于具有有限个等式和不等式约束的拟可微优化,给出了一个与特殊对象选取无关的次线性的Lagrange乘子法则,推广了已有的结果.Lagrange muliplier type optimality conditions for constrained quasidifferentiable programming usually depend on the choice of special objects（super-gradient, direction ,and so on）, which is one of the key problems for constrained quasidifferentiable programming. In this paper,applying Minkowski duality of convex compact sets and sublinear functions, the sublinear Lagrange multiplic rule for quasidifferentiable optimization with a finite number of inequality and equality constraints are deduced by the nonlinear Lagrange function generated by a sublinear function,which improves the existing results.

关 键 词：运筹学 拟可微优化 最优性条件 LAGRANGE乘子 次线性 

分 类 号：O224[理学—运筹学与控制论]