﻿ 拟凸优化问题严格解的最优性必要条件 Necessary Optimality Conditions of Strict Solutions for Quasiconvex Optimization Problems

Vol. 08  No. 03 ( 2019 ), Article ID: 29137 , 7 pages
10.12677/AAM.2019.83045

Necessary Optimality Conditions of Strict Solutions for Quasiconvex Optimization Problems

Linting Li, Ming Yang, Ying Gao

School of Mathematical Sciences, Chongqing Normal University, Chongqing

Received: Feb. 11th, 2019; accepted: Feb. 27th, 2019; published: Mar. 6th, 2019

ABSTRACT

In this paper, we study the necessary conditions of strict solutions for quasiconvex optimization problems by using the subdifferential of quasiconvex function. Firstly, we introduce the basic concepts of quasiconvex optimization problem. Then, we derive the necessary conditions of the strict solutions for quasiconvex optimization problems.

Keywords:Quasiconvex Optimization Problems, Strict Solution, Optimality Condition

1. 引言

2. 预备知识

ii) 当时，(MOP)为多目标问题。若存在，对任意满足

3. 拟凸条件下严格解的最优性必要条件

，则由上式左边可知，令，则由上式右边可知，因此。故有。由不是f在上的局部弱有效解且可知。因为，所以存在，使得，所以

，取，则。因此，但

，又因为，从而有。故由凸集分离定理可知，存在使得

，则由上式左边可知，令，则由上式右边可知，因此。故有。由不是f在上的局部弱有效解且可知，从而由法锥的运算法则有。又因为处为 Gutierrez函数，所以。因为，所以存在和不全为零的，使得。故有

。取，这时有

，有。但不是严格解。

4. 带有不等式约束的拟凸条件下严格解的最优性必要条件

i) 存在使得

ii) 对是闭的，的对角线。

Necessary Optimality Conditions of Strict Solutions for Quasiconvex Optimization Problems[J]. 应用数学进展, 2019, 08(03): 400-406. https://doi.org/10.12677/AAM.2019.83045

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