【摘要】：當(dāng)目標(biāo)函數(shù)和約束函數(shù)構(gòu)成的序偶映射是近似錐-次類凸時(shí),在較弱的約束品性假設(shè)下,借助凸集分離定理得到了集值優(yōu)化逼近嚴(yán)有效解的拉格朗日型最優(yōu)性條件.在Banach空間中,研究集值優(yōu)化問題的逼近嚴(yán)有效解的優(yōu)化條件.利用Ioffe引進(jìn)的預(yù)導(dǎo)數(shù)概念,借助集值映射的預(yù)導(dǎo)數(shù)的存在性,建立集值優(yōu)化問題的逼近嚴(yán)有效解的充分必要條件.當(dāng)目標(biāo)函數(shù)和約束函數(shù)均M-可導(dǎo)時(shí),在目標(biāo)函數(shù)和約束函數(shù)構(gòu)成的序偶映射是近似錐-次類凸的假設(shè)下,借助凸集分離定理給出了具有約束的向量均衡問題(VEPC)中的弱有效解的充分和必要條件.
[Abstract]:When the ordered pair mapping of objective function and constraint function is approximately cone-subconvex, the Lagrangian optimality condition for set-valued optimization approximation to strict efficient solution is obtained by means of convex set separation theorem under the assumption of weak constraint character. In Banach space, the optimization conditions for approximating strict efficient solutions of set-valued optimization problems are studied. By using the concept of prederivative introduced by Ioffe and the existence of prederivative of set-valued mappings, the sufficient and necessary conditions for the approximation of strict efficient solutions of set-valued optimization problems are established. When the objective function and the constraint function are M-differentiable, under the assumption that the ordered pair mapping of the objective function and the constraint function is approximately cone-subconvex, By means of the separation theorem of convex sets, the necessary and sufficient conditions for weak efficient solutions of vector equilibrium problems with constraints in (VEPC) are given.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O224

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