拟不变凸集值优化的Kuhn-Tucker条件与Wolfe对偶  

Kuhn-Tucker Condition and the Wolfe Duality of Preinvex Set-Valued Optimization

作　　者：盛宝怀[1] 刘三阳[2] 张石生（推荐） 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000 [2]西安电子科技大学应用数学系,浙江绍兴312000 [3]不详

出　　处：《应用数学和力学》2006年第12期1447-1456,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10371024);浙江省自然科学基金资助项目(Y604003)

摘　　要：研究了拟不变凸集值优化最优性的Kuhn-Tucker条件及Wolfe型对偶问题·首先引进了al-pha-阶G-拟不变凸集和alpha-阶S-拟不变凸集值函数的概念,由此研究了alpha-阶G-拟不变凸集所对应的伴随切锥及alpha-阶伴随导数的性质;最后,借助alpha-阶伴随切导数刻画了alpha-阶S-拟不变凸集值优化最优性的Kuhn-Tucker条件和Wolfe型对偶·The optimality Kuhn-Tucker condition and the Wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order Spreinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied; Then, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

关 键 词：拟不变凸集值函数 伴随上图导数 最优性条件 对偶 

分 类 号：O221.6[理学—运筹学与控制论]