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| 广义半无限规划新的最优性条件 | |
| 引用本文： | 周金川,王长钰,刘丙状,李梅霞. 广义半无限规划新的最优性条件[J]. 运筹学学报, 2009, 13(1) |
| 作者姓名： | 周金川 王长钰 刘丙状 李梅霞 |
| 作者单位： | 周金川,Zhou Jinchuan(Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China);王长钰,Wang Changyu(Institute of Operations Research, Qufu Normal University, Qufu 273165, China);刘丙状,Liu Bingzhuang(School of Science, Shandong University of Technology, Zibo 255049, China);李梅霞,Li Meixia(School of Mathematics and Information Science, Weifang University, Shandong 261061, China) |
| 摘 要： | 本文讨论了一类指标集依赖于决策变量的广义半无限规划(GSMMP).首先通过刻画目标函数的Clarke导数和Clarke次微分,建立其一阶最优性条件.其次,通过对下层问题Q(x)进行扰动分析,我们得到Q(x)的一个精确罚表示.由此,利用一组精确罚函数将(GSMMP)转化为经典的半无限极大极小规划,从而可利用已有的经典半无限规划的算法来对(GSMMP)进行求解. |
| 关 键 词： | 运筹学 广义半无限极大极小规划 罚函数 一阶最优性条件 |
New Optimality Conditions for Generalized Semi-Infinite Min-Max Programming |
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| Zhou Jinchuan,Wang Changyu,Liu Bingzhuang,Li Meixia. New Optimality Conditions for Generalized Semi-Infinite Min-Max Programming[J]. OR Transactions, 2009, 13(1) | |
| Authors: | Zhou Jinchuan Wang Changyu Liu Bingzhuang Li Meixia |
| Affiliation: | 1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China 2. Institute of Operations Research, Qufu Normal University, Qufu 273165, China 3. School of Science, Shandong University of Technology, Zibo 255049, China 4. School of Mathematics and Information Science, Weifang University, Shandong 261061, China |
| Abstract: | This paper deals with a class of generalized semi-infinite min-max pro-gramming (GSMMP), in which the index set depends on the decision variable. Based on some new characterizations of the Clarke derivative and Clarke subdifferential of the ob-jective function, we develop the first-order optimality conditions for (GSMMP) in terms of second-order multipliers. Moreover, by addressing the perturbed problem of the lower-level programming Q(x), we obtain an exact penalty representations for Q(x), which allows us to convert (GSMMP) into the standard semi-infinite rain-max programming via a class of exact penalty functions. This fact makes it possible to solve (GSMMP) by using any available standard semi-infinite optimization algorithms. |
| Keywords: | Operations research generalized semi-infinite rain-max programming penalty function first-order optimality conditions |
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