赵洁
【摘 要】G-不变凸函数是一类新的广义凸函数,是G-凸函数的推广。本文研究了一类多目标半无限规划问题,在G-不变凸性条件下,建立了该类问题有效解的Karush-Kuhn-Tucker充分条件。本文的结果是后续对偶理论研究的基础。
【关键词】多目标规划;半无限规划;G-不变凸;最优性条件
【Abstract】G-invex functions is a class of generalized convex functions. It is a generalization of the G-convex functions. In this paper, a class of multiobjective semi-infinite programming problems is considered. Karush-Kuhn-Tucker sufficient optimality condition of efficient solution for such problem are established under the assumption of G-invexity. The results of this paper is the basis of subsequent duality theory research.
【Key words】Multi-objective programming problem; Semi-infinite programming problem; G-invex function; Optimality conditions
凸性和广义凸性在最优化理论和应用中有深远的影响。1981年,Hanson在文献[1]中提出不变凸函数的概念。2007年,Antczak在文献[2]中提出一类实值G-不变凸函数。随后Antczak将它推广到向量情形,并且用它研究了一类多目标规划的最优性条件和对偶[3-4]。
半无限规划(SIP)是指决策变量有限而约束函数无限的优化问题。Kanzi和 Nobakhtian 在[5]中证明了等式约束下的SIP的充分必要最优性条件。S.K.Mishra等在[6]中研究了一类非光滑半无限的对偶理论。
受以上文献启发,本文主要研究G-不变凸函数下一类多目标半无限规划的最优性条件。
【参考文献】
[1]Hanson. On sufficiency of the Kuhn-Tucker conditions[J]. Journal of Mathematical Analysis and Applications, 1981, 80(2): 545-550.
[2]Antczak. New optimality conditions and duality results of G-type in differentiable mathematical programming[J]. Nonlinear Analysis, 2007, 66: 1617-1632.
[3]Antczak. On G-invex multiobjective programming. Part I. Optimality[J]. Journal of Global Optimization, 2009, 43(1): 97-109.
[4]Antczak. On G-invex multiobjective programming. Part II. Duality[J]. Journal of Global Optimization, 2009, 43(1):111-140.
[5]Kanzi,Nobakhtian. Optimality conditions for non-smooth semi-infinite programming[J]. Optimization, 2010, 59(5): 717-727.
[6]Mishra,Jaiswal,LeThi. Duality for nonsmooth semi-infinite programming problems[J]. Optimization Letter, DOI 10.1007/s11590-010-0240-8.
[7]林锉云,董加礼.多目标优化的方法与理论[M].吉林:吉林教育出版社,1992.
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