本文關(guān)鍵詞：廣義強(qiáng)凸多目標(biāo)優(yōu)化的最優(yōu)性條件研究　出處：《北方民族大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

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【摘要】：強(qiáng)凸性在最優(yōu)化理論及其應(yīng)用研究中扮演著非常重要的角色,本論文針對(duì)這類(lèi)凸性及在多目標(biāo)等領(lǐng)域展開(kāi)研究.主要研究?jī)?nèi)容包括以下三個(gè)部分:第一部分,向量變分不等式與無(wú)約束非光滑多目標(biāo)優(yōu)化問(wèn)題關(guān)系:首先對(duì)Lischitz向量值函數(shù)在強(qiáng)凸性概念的基礎(chǔ)上,引入了一類(lèi)高階廣義強(qiáng)偽凸性,稱(chēng)之為m-階強(qiáng)偽凸型-I函數(shù),并給出具體實(shí)例說(shuō)明了這類(lèi)函數(shù)是存在的.其次,在函數(shù)的m-階強(qiáng)偽凸型-I假設(shè)下,研究了無(wú)約束非光滑多目標(biāo)優(yōu)化問(wèn)題(NMOP)的m-階嚴(yán)格最小解、向量關(guān)鍵點(diǎn)和弱向量變分不等式的解之間的關(guān)系.第二部分,不等式約束的非光滑多目標(biāo)優(yōu)化問(wèn)題的最優(yōu)性條件:我們首先在高階強(qiáng)偽凸型-I函數(shù)條件下研究了帶不等式約束的非光滑多目標(biāo)優(yōu)化問(wèn)題(CNMOP)的局部高階嚴(yán)格最小解是全局高階嚴(yán)格最小解,以及問(wèn)題(CNMOP)的最優(yōu)性充分條件.其次,在Guignard約束規(guī)格和Abadie約束規(guī)格的基礎(chǔ)上給出了廣義Guignard約束規(guī)格和廣義Abadie約束規(guī)格,研究了問(wèn)題(CNMOP)的最優(yōu)性必要條件.最后,我們研究了問(wèn)題(CNMOP)的部分Lagrangian向量值函數(shù)的m-階混合鞍點(diǎn),并且在m-階強(qiáng)偽凸型-I的假設(shè)下證明了m-階混合鞍點(diǎn)和高階嚴(yán)格最小解是等價(jià)的.第三部分,內(nèi)積空間中的h-強(qiáng)凸集值映射:首先在賦范線(xiàn)性空間中引入了一類(lèi)廣義強(qiáng)凸集值映射,稱(chēng)之為h-強(qiáng)凸集值映射.其次利用R(?)dstr(?)m消去律研究了h-強(qiáng)凸集值映射的一些基本性質(zhì).最后,給出了h-強(qiáng)凸集值映射形式下賦范線(xiàn)性空間為內(nèi)積空間的刻畫(huà)條件.
[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.

【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O221.6

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本文編號(hào)：1378105