Abstract: Concepts of generalized strict pseudoconvexity, generalized quasiconvexity and generalized weak quasiconvexity are introduced; Properties and relations between these generalized convex functions are investigated, and Kuhn-Tucker sufficient conditions are proven for nondifferentiable programming under some weaker conditions.

Key words: nondifferentiable programming, generalized convex functions, sufficient conditions

摘要： 本文引入了广义严格伪凸函数,广义伪凸函数,广义拟凸函数和广义弱拟凸函数。并讨论了它们之间的关系及性质。在这些广义凸性条件下,证明了不可微规划极值的Kuhn-Tucker充分条件。

关键词: 不可微规划, 广义凸函数, 充分条件