【作者】 宋虹颖；

【导师】 景书杰；

【作者基本信息】 河南理工大学 ， 应用数学， 2009， 硕士

【摘要】 E -凸集、E -凸函数、半E -凸函数和拟E -凸函数是凸集和凸函数的推广.这些集合和函数近年来被广泛应用于许多规划问题.借助于这些集合和函数的定义思想,本文定义了E -凸锥、伪拟E -凸函数、E -凸函数方向导数等几种更广义的概念.首先讨论了E -凸集、E -凸锥的性质.随后,讨论了定义在实线性空间中的E -凸集上的实值E -凸函数、半E -凸函数、伪拟E -凸函数、E -凸函数方向导数的性质.这是第二章、第三章、第四章的内容.在第五章中,给出了E -次微分的存在性定理,在此基础上,本文研究了E -次微分共轭性,连续性,以及单调性.第六章中,讨论了E -凸规划问题.更多还原

【Abstract】 E -convex set and E -convex function are the promotion of convex set and convex function. Those kinds of sets and functions are applied to many mathematical programming problems in rencent years.In this paper, with the aid of idea of defining those sets and functions, the definitions of E -convex cone, pseudo-quasi- E -convex functions, E -direction derivative are discussed. Firstly, we consider the properties of E -convex set and E -convex cone.The properties of real E -convex function, semi- E -convex functions, pseudo-quasi- E -convex functions, E -direction derivative defined on a E -convex set in the real liner spaces are discussed. Those are prime in Chapter two, Chapter three and Chapter four.In Chapter five, the Existence theorem of E -direction derivative is given .Under the assumption, conjugation, continuity, monotonicity of E -Subdifferential are studied .In Chapter six , we discuss E - convex-programming problems.更多还原