非可微分二层Lipschitz规划的广义微分和广义方向导数  

GENERALIZED DIRECTIONAL DERIVATIVE AND DIFFERENTIAL OF NONDIFFERNTIABLE TWO LEVEL LIPSCHITZ PROGRAMMING

作　　者：王先甲[1] 冯高友[1] 

机构地区：[1]武汉水利电力大学

出　　处：《数学杂志》1999年第1期71-78,共8页Journal of Mathematics

基　　金：国家教委博士点基金;湖北省自然科学基金

摘　　要：本文对构成函数为Ｌｉｐｓｃｈｉｔｚ函数的二层规划问题，利用非光滑分析工具，讨论了下层极值函数和上层复合目标函数的Ｌｉｐｓｃｈｉｔｚ连续性，给出了这些函数的广义微分和广义方向导数的估计式．本文得到的结果为进一步研究非可微二层Ｌｉｐｓｃｈｉｔｚ规划的最优性条件和有效算法等理论和方法问题奠定了基础．This paper discusses Lipschitz continuity of optimal value functions at lower level and compound objective function at upper level in the nondifferentiable two level Lipschitz programming, whose conponent functions are Lipschitz continuous, by using nonsmooth analysis theory. Estimate formulae of generalized divrectional derivative and differential of the functions are given. The results obtained in this paper lays a foundation to further study optimality conditions and efficient algorithms of the nondifferentiable two level Lipschitz programming.

关 键 词：二层规划 广义微分 广义方向导数 李普希兹函数 

分 类 号：O221[理学—运筹学与控制论]