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中文摘要：
本文在邻近锥次似凸性假设下,建立了集值映射向量优化问题ε-弱有效解的Lagrange乘子定理。首先,利用择一性定理,给出了集值优化问题ε-弱有效解的一个必要性条件。进一步,建立了集值优化问题ε-弱有效解的充分必要条件。最后,在邻近次似凸性假设下,建立了集值映射向量优化问题ε-弱有效解的Lagrange乘子定理。本文的主要结果推广了已有文献中的相应结果到近似解的情形,同时将次似凸性条件减弱到邻近次似凸的假设下。
英文摘要：
In this paper, we establish a Lagrangian multiplier theorem of ε-weakly efficient solutions in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlike. Firstly, a necessary condition of e-weakly efficient solu-tions is given in vector optimization problems with set-valued maps using an alternative theorem. Moreover, a sufficient and necessa-ry condition of s-weakly efficient solutions is given. Finally, under the assumption of nearly cone-subconvexlike, a Lagrangian multi-plier theorem of ε-weakly efficient solutions is established for vector optimization problems with set-valued maps. The main results in this article extend the corresponding results in [6] to the approximate and meanwhile the convexity condition of [6] is reduced to the nearly cone-subconvexlike assumptions.
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