一类伪线性优化问题解集的刻画  

Characterizations of the Solution Set for a Class of η-pseudolinear Programming

作　　者：陈林[1] 龙莆均[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2013年第1期30-32,共3页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市教委科技研究项目(No.KJ100608);重庆市自然科学基金项目(No.CSTC2010BB2090)

摘　　要：凸和广义凸在数理经济、工程学、管理科学和最优化理论中有着很重要的地位。本文在广义不变凸性下主要研究了一类非线性优化问题解集的刻画。文中利用了Dini上方向导数和Lagrange乘子研究了一类带约束的η-伪线性优化问题解集的刻画。首先在Dini上方向导数的背景下,给出了此类带约束的非可微伪线性规划问题的一些性质;然后在一定条件下证明了此类问题的可行集和最优解集是不变凸的;最后利用Dini上方向导数和Lagrange乘子得到了最优解集的一些等价刻画。Convexity and the generalized convexity play a very important role in mathematical economic, engineering, management science and optimization theory. This paper is concerned with the properties and characterizations of solution sets for a class of non linear optimizations under the invexity and generalized invexity. In this paper, we focus on the characterizations of solution sets for η-pseudolinear programming by the Dini upper directional derivative and Lagrange multiplier. First, some properties are given for the nondifferentiable pseudolinear programming with constraints under the Dini upper directional derivative. And in certain condi tions, the optimal solution set and feasible set is invex for such problems. Finally, some characterizations of the solution set arc proved via the Dini upper directional derivative and Lagrange multiplier.

关 键 词：η-伪线性优化问题 Dini上方向导数 解集刻画 LAGRANGE乘子 

分 类 号：O221.2[理学—运筹学与控制论]