非凸非光滑规划的最优性与对偶性

Optimality and Duality of Nonconvex and Nonsmooth Programming

利用Ｃｌａｒｋｅ广义梯度定义的Ｌｉｐｓｃｈｉｔｚ函数的广义凸性条件，首先讨论了非凸非光滑多目标规划的最优性，建立了其充分性条件与Ｋｕｈｎ－Ｔｕｃｋｅｒ型必要条件；然后讨论了非凸非光滑单目标规划的广义Ｍｏｎｄ－Ｗｅｉｒ型对偶，建立了相应的弱对偶定理、强对偶定理及逆对偶定理．

By means of the generalized convexity conditions for Lipschitzs function defined by Clarke generalized gradient, the optimality for nonconvex and nonsmooth multiobjective programming is discussed. The sufficient conditions and Kuhn Tucker type necessary conditions are established. The generalized Mond Weir type duality for nonconvex and nonsmooth single objective programming is also discussed with the weak duality theorem, strong duality theorem and converse duality theorem established. The results cover many already known optimality conditions and duality theorems