广义凸条件下一类多目标优化问题的对偶  

Duality for a kind of multiobjective optimization problem under generalized convexity

作　　者：张瑞芳[1] 王海军[1] 

机构地区：[1]太原师范学院数学系,太原030012

出　　处：《沈阳师范大学学报（自然科学版）》2014年第4期482-485,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11171250)

摘　　要：凸性是最优化理论中最常用的假设之一。在实际应用中目标函数的性质可能不是那么理想,为了减弱凸性要求,人们给出了各种各样的广义凸性概念。近年来,广义凸性成为数学优化研究的新发展趋势,越来越多的学者致力于讨论在各种广义凸性条件下多目标优化问题的对偶结论及其应用。在广义凸条件之下考察一类多目标优化问题,首先介绍一类广义凸函数的概念及相关性质。然后建立了多目标优化问题(即原问题)的Wolfe对偶模型,在广义凸条件下得到了原问题与Wolfe对偶问题之间的弱对偶,强对偶和逆对偶定理。最后建立了多目标优化问题的混合型对偶模型,并且得到了原问题的混合型对偶问题的弱对偶,强对偶和逆对偶定理。Convexity is the most commonly used hypothesis in optimization theory. In the practical application, the property of objective function is not so ideal. In order to relax the convexity condition, people provide various of generalized convexity concepts. In recent years, generalized convexity become the new trend of mathematical optimization, more and more scholars devote to discuss multiobjective optimization problem duality results and its applications under generalized convexity. This paper considers a kind of multiobjective optimization problem under generalized convexity condition. Firstly, we introduce the concept of a kind of generalized convexity and related properties. Then we set up Wolfe dual problem of the original multiobjective optimization problem. Weak, strong and converse duality results between the original problem and its Wolfe dual problem are given. Finally we establish mixed type dual problem of the original problem, and obtain weak, strong and converse duality between the original problem and its mixed type dual problem.

关 键 词：广义凸函数 多目标优化 Wolfe对偶 混合型对偶 

分 类 号：O221.6[理学—运筹学与控制论]