一类半可微优化问题的解集

运筹与管理 ›› 2011, Vol. 20 ›› Issue (2): 1-6.

• 理论分析与方法探讨 • 下一篇

一类半可微优化问题的解集

薛声家, 杨凡, 张先郁

暨南大学管理学院,广东广州 510632

收稿日期:2010-09-29 出版日期:2011-04-25
作者简介:薛声家(1944-),男,广东潮阳人,教授,博士生导师,研究方向:管理科学与管理决策、最优化;杨凡,张先郁,管理学院博士研究生。
基金资助:
“211工程”子项目(50630060);广东省教育厅科研重大项目(20060914009)

Solution Sets of a Class of Semidifferentiable Optimization Problems

XUE Sheng-jia, YANG Fan, ZHANG Xian-yu

School of Management, Jinan University, Guangzhou 510632, China

Received:2010-09-29 Online:2011-04-25

摘要/Abstract

摘要： 本文考虑线性约束条件下连续与半可微的伪线性(既伪凸又伪凹)函数的优化问题.使用伪线性函数的性质推导了解集的一般表达式,并基于用右侧导数代替既约梯度的广义凸单纯形法,给出了唯一解的条件以及当唯一性条件不满足时求出解集的计算步骤,最后给出了算例。

关键词: 非线性优化, 解集, 广义凸单纯形法, 半可微函数, 伪线性, 右侧导数

Abstract: The problem of optimizing a continuous and semidifferentiable pseudolinear(both pseudoconvex and pseudoconcave)function with linear constraints is considered. By means of the properties of pseudolinearity, the general expression for the solution set is derived. Based on the extended convex simplex method that uses right-sided derivatives instead of reduced gradient vector, the uniqueness condition of the solution and the computational procedure to find out the solution set(if the uniqueness condition is not satisfied)are provided. Finally, an illustrative example is also given.

Key words: nonlinear optimization, solution set, extended convex simplex method, semidifferentiable function, pseudolinearity, right-sided derivative

中图分类号:

O221.2

薛声家, 杨凡, 张先郁. 一类半可微优化问题的解集[J]. 运筹与管理, 2011, 20(2): 1-6.

XUE Sheng-jia, YANG Fan, ZHANG Xian-yu. Solution Sets of a Class of Semidifferentiable Optimization Problems[J]. Operations Research and Management Science, 2011, 20(2): 1-6.

参考文献

[1] 郑义建.线性规划问题最优解集的结构与仅有唯一最优解的充分条件[J].应用数学与计算数学学报,1992,6(1):42-46.
[2] 张新辉.有无穷多最优解线性规划问题[J].运筹与管理,1995,4(1):1-4.
[3] 李军.线性规划无穷多最优解的讨论[J].运筹与管理,1999,8(1):87-92.
[4] 薛声家,左小德.确定线性规划全部最优解的方法[J].数学的实践与认识,2005,35(1):101-105.
[5] 魏权龄,闫洪.广义最优化理论和模型[M].北京:科学出版社,2003.
[6] Mangasarian O L. A simple characterization of solution sets of convex programs[J]. Operations Research Letters, 1988, 8(1): 21-26.
[7] Burke J V, Ferris M C. Characterization of solution sets of convex programs[J]. Operations Research Letters, 1991, 10(1): 57-60.
[8] Jeyakumar V, Yang X Q. On characterizing the solution sets of pseudolinear programs[J]. J. Optimization Theory and Applications, 1995, 87: 747-755.
[9] Lu Qihui, Zeng Lifei. Characterizations of solution sets of pseudolinear programs[J]. Journal of Fudan University, 2004, 43(1): 130-134.
[10] Xue Shengjia. Determining the optimal solution set for linear fractional programming[J]. J. Systems Engineering and Electronics, 2002, 13(3): 40-45.
[11] Xue Shengjia. On alternative optimal solutions to quasimonotonic programming with linear constraints[J]. Applied Mathematics J. Chinese Univ.Ser.B, 2007, 22(1): 119-125.
[12] Avriel M. Nonlinear Programming: Analysis and Methods[M]. New Jersey: Prentice Hall Ins.1976.
[13] Yang X Q. Vector variational inequality and Vector pseudolinear optimization[J]. J. Optimization Theory and Applications, 1997, 95: 729-734.
[14] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear programming : Theory and algorithms ,3rd Edition[M]. New York: John Wiley & Sons, 2006.

一类半可微优化问题的解集

Solution Sets of a Class of Semidifferentiable Optimization Problems

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

编辑推荐

Metrics

[1]	崔春生, 贾明泽, 葛敬云, 李天鹏, 孟鹏洋. 基于Selectope解集和局中人最大满意度的合作对策解的研究[J]. 运筹与管理, 2021, 30(7): 23-28.
[2]	刘国山, 丁冰洁, 刁海璨. 一类非单调互补问题的Canonical对偶问题研究[J]. 运筹与管理, 2021, 30(1): 1-5.
[3]	谷新军, 郭秀萍. 随机混流U型拆卸线平衡排序问题多目标进化算法优化[J]. 运筹与管理, 2017, 26(9): 52-61.
[4]	姜璇,邓世名,李沿海. 考虑线下渠道时销售商在团购网站上的最优销售策略研究[J]. 运筹与管理, 2016, 25(3): 46-56.
[5]	熊轶, 陈智民, 霍佳震, 潘燕春, 周明. 总量控制和交易环境下考虑随机需求的企业决策分析[J]. 运筹与管理, 2015, 24(6): 25-33.
[6]	郭春香, 龚浩, 郭耀煌. 区间信度环境下基于偏好熵的随机格序排列方法[J]. 运筹与管理, 2013, 22(3): 21-29.