Exhauster广义凸函数及其在非光滑规划中的应用

摘要

利用次微分Exhauster定义一类新的广义凸函数,包括上Exhauster凸和下Exhauster 凸,并利用函数的这种广义凸性,对无约束非光滑极小值和极大值问题,证明了在上Exhauster凸和下Exhauster凸性条件下最优性必要条件的充分性.%A new class of generalized convex functions were defined by using differential Exhausters,including upper Exhauster convex function and lower Exhauster convex function.By using the generalized convexity of functions,we proved the sufficiency of the necessary conditions of optimality under the condition of upper Exhauster convexity and lower Exhauster convexity for unconstrained nonsmooth minimum and maximum problems.