逼近严有效解和弱有效解的若干最优性条件
发布时间：2018-12-09 17:01
【摘要】：当目标函数和约束函数构成的序偶映射是近似锥-次类凸时,在较弱的约束品性假设下,借助凸集分离定理得到了集值优化逼近严有效解的拉格朗日型最优性条件.在Banach空间中,研究集值优化问题的逼近严有效解的优化条件.利用Ioffe引进的预导数概念,借助集值映射的预导数的存在性,建立集值优化问题的逼近严有效解的充分必要条件.当目标函数和约束函数均M-可导时,在目标函数和约束函数构成的序偶映射是近似锥-次类凸的假设下,借助凸集分离定理给出了具有约束的向量均衡问题(VEPC)中的弱有效解的充分和必要条件.
[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.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224
本文编号：2369732
[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.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224
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