广义强凸多目标优化的最优性条件研究

发布时间：2018-01-04 10:21

本文关键词：广义强凸多目标优化的最优性条件研究　出处：《北方民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：强凸性在最优化理论及其应用研究中扮演着非常重要的角色,本论文针对这类凸性及在多目标等领域展开研究.主要研究内容包括以下三个部分:第一部分,向量变分不等式与无约束非光滑多目标优化问题关系:首先对Lischitz向量值函数在强凸性概念的基础上,引入了一类高阶广义强伪凸性,称之为m-阶强伪凸型-I函数,并给出具体实例说明了这类函数是存在的.其次,在函数的m-阶强伪凸型-I假设下,研究了无约束非光滑多目标优化问题(NMOP)的m-阶严格最小解、向量关键点和弱向量变分不等式的解之间的关系.第二部分,不等式约束的非光滑多目标优化问题的最优性条件:我们首先在高阶强伪凸型-I函数条件下研究了带不等式约束的非光滑多目标优化问题(CNMOP)的局部高阶严格最小解是全局高阶严格最小解,以及问题(CNMOP)的最优性充分条件.其次,在Guignard约束规格和Abadie约束规格的基础上给出了广义Guignard约束规格和广义Abadie约束规格,研究了问题(CNMOP)的最优性必要条件.最后,我们研究了问题(CNMOP)的部分Lagrangian向量值函数的m-阶混合鞍点,并且在m-阶强伪凸型-I的假设下证明了m-阶混合鞍点和高阶严格最小解是等价的.第三部分,内积空间中的h-强凸集值映射:首先在赋范线性空间中引入了一类广义强凸集值映射,称之为h-强凸集值映射.其次利用R(?)dstr(?)m消去律研究了h-强凸集值映射的一些基本性质.最后,给出了h-强凸集值映射形式下赋范线性空间为内积空间的刻画条件.
[Abstract]:Strong convexity plays a very important role in the study of optimization theory and its application, this paper focuses on the convexity and expansion in multi-objective field. The main research contents include the following three parts: the first part, inequality and unconstrained Nonsmooth Multiobjective Optimization Problems: firstly, Lischitz vector relationship based on the vector valued function strong convexity concept, introduced a kind of high order generalized strong pseudo convexity, called m- order pseudo convex type -I function, and give specific examples of this type of function is exist. Secondly, in order to m- strongly pseudo convex function -I assumption. Study on unconstrained Nonsmooth Multiobjective Optimization Problems (NMOP) m- order strict minimal solution vector, the key point and the weak vector variational inequality relation between solutions. In the second part, the optimality conditions of inequality constrained Nonsmooth Multiobjective Optimization Problems: first in the US Good coincidence conditions of pseudo convex type -I function studied with inequality constraint Nonsmooth Multiobjective Optimization Problems (CNMOP) of the local high order strict minimal solution is the global minimum solution of high order strictly, and (CNMOP) the sufficient optimality conditions. Secondly, based on Guignard constraint specification and Abadie constraint specifications are the generalized Guignard constraint specification and generalized Abadie constraint specification, on the issue of (CNMOP) the necessary optimality conditions. Finally, we study the problem of (CNMOP) part of Lagrangian vector valued m- order mixed saddle point function, and in the pseudo convex order m- type -I under the assumption that m- order saddle point high order and strict minimal solutions are equivalent. The third part, the inner product space of h- set-valued maps: first in a normed linear space is introduced in a class of generalized strongly convex set-valued mapping, called h-. The set-valued mapping using R (?) dstr (?) M We study some basic properties of h- strongly convex set valued mappings. Finally, we give the characterizations of normed linear spaces for inner product spaces under the form of h- strongly convex set valued maps.

【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221.6

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