Solution Sets of a Class of Semidifferentiable Optimization Problems

Operations Research and Management Science ›› 2011, Vol. 20 ›› Issue (2): 1-6.

• Theory Analysis and Methodology Study • Next Articles

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

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

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)

Abstract

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

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

CLC Number:

O221.2

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.

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.

References

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Solution Sets of a Class of Semidifferentiable Optimization Problems

一类半可微优化问题的解集

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