| | | | | 广义凸性下多目标优化 | | | 雷晓军;梁治安 | | | 严格凸优化问题在理论上已证明有唯一的全局最优解,并且可应用快速的多项式时间算法和软件求解这一全局最优解。所有的优化问题都体现出凸性,故优化问题的分水岭不是线性与非线性,而是凸性与非凸性[14]。本文叙述了广义凸性下部分研究成果,广义凸函数是凸函数的弱化及推广,它与函数数的作用一样,当目标函数或约束条件是具备某些广义凸性,即拟凸、伪凸,似不变凸等条件时,也能获得多目标规划的最优有效解,相应地也可得到弱对偶和强对偶的一些结果。
【作者单位】：铜仁学院数学系 贵州铜仁554300(雷晓军);上海财经大学应用数学系 上海200433(梁治安)
【关键词】：拟(伪)凸;拟(伪)不变凸;有效解;弱(强)对偶
【分类号】：O221.6
【DOI】：CNKI:ISSN:1671-9972.0.2006-06-018
【正文快照】：
1.引言从20世纪60年代起,人们就已经认识到凸优化的非常好的特性,((1)局部最小就是全局最小,(2)求解复杂的凸优化问题可以转化为求解较简单的对偶问题等),优化问题所涉及到的目标函数从单目标到多目标,人们利用广义代数运算,由(F,ρ)-凸的概念(见V.Preda[15])提出是F-凸[16]和ρ-凸[17]的扩展,多目标规划问题.,()0(Mop):min()(1(),2(),())≤=ΔstgxfxfxfxLf px(其中,X 0是R n中的开集,fi:X0→R,gi:X 0→Rm是可微的)的有效解性质由V.Jegukumar and Mond[3]获得了一些结果,并且Z.A.Liang,H.X.Huang和P.M.Pardalos[7-9]进一步拓展到… | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | Multi-Objective Optimization with General Convexity | | | LEI Xiao-jun1;LIANG Zhi-an2(1.Department of Mathematics;TU.Tongren;Guizhou 554300;China 2.Shanghai Economics and Finance University;Shanghai 220043;China) | | | The problems of rigorous optimization of convex has been proved on the theory that there is an unique optimization which can be a solution through a quick multiple calculations with time and software.All the problems of optimization show the convexity that the boundary of optimization is not linear and non-linear but convex and non-convex.Parts of the achievements of general convexity show that general convex function is weakening and popularization of general convex function.With the same function as the figure of function,as the objective function or limited condition is provided with general convexity,such as an imitation convexity,a false convexity,and a constant convexity.It also can gain the most effective solution planned by the multi-objective to get relatively results from less dual to much dual.
【Keyword】：an imitation(false) convexity;a(false) constant convexity;an effective solution;less(much) dual |
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