非光滑(h,ψ)-半无限规划解的充分性和对偶性  

ON SUFFICIENCY AND DUALITY OF SOLUTIONS FOR NONSMOOTH(h,ψ)-SEMI-INFINITE PROGRAMMING

作　　者：张庆祥[1] 

机构地区：[1]延安大学数学与计算机系,延安716000

出　　处：《应用数学学报》2001年第1期129-138,共10页Acta Mathematicae Applicatae Sinica

基　　金：陕西省自然科学基金(98SL07);陕西省教委专项科研基金(98JK076)资助项目.

摘　　要：本文利用 Ｂｅｎ－Ｔａｌ广义代数运算和广义（ｈ，）－梯度；提出了几类非光滑非凸函数（广义（ｈ，）概念，研究了这些新广义凸性的一些性质，讨论了这些新广义凸性与一些已有的凸性之间的关系，分别给出了三个（ｈ，）－伪凸或（ｈ，）－拟凸但不是凸函数、也不是某些广义凸函数的例子．在是严格递增连续函数，并且（０）＝０相当弱的假设下，得到了一类非光滑（ｈ）半无限规划的一些最优性充分条件和几个对偶性结果．In this paper, several concepts of nonsmooth nonconvex functions (generalized (h, ψ )-convex) are presented by using Ben-Tal's algebraic generalized operations and generalized (h, ψ)-gradient. The properties of these new generalized convex functions are studied. The relationships of these new generalized convexities and some well-know convexities are discussed. Three examples are given which are (h, ψ )-pseudoconvex or (h, ψ)-quasiconvex, but are neither convex nor some generalized convex functions, respectively. And then some optimality sufficient conditions and several duality results for a class of nonsmooth (h, ψ)- semi-infinite programming are obtained under the weak assumptions that is strictly increasing continuous function and that

关 键 词：非光滑 半无限规划 充分性 对偶性 (h ψ)-凸函数 

分 类 号：O221[理学—运筹学与控制论] O224[理学—数学]