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非光滑向量均衡问题近似拟全局真有效解的最优性条件

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非光滑向量均衡问题近似拟全局真有效解的最优性条件 韩文艳, 余国林北方民族大学应用数学数学研究所, 银川, 750021 Optimality Conditions for Approximate Quasi Globally Proper Efficient Solutions to Nonsmooth Vector Equilibrium Problems HAN Wenyan, YU GuolinInstitute of Applied Mathematics, North Minzu University, Yinchuan 750021, China
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摘要本文研究一类非光滑向量均衡问题(Vector Equilibrium Problem)(VEP)关于近似拟全局真有效解的最优性条件.首先,利用凸集的拟相对内部型分离定理和Clarke次微分的性质,得到了问题(VEP)关于近似拟全局真有效解的最优性必要条件.其次,引入近似伪拟凸函数的概念,并给出具体实例验证其存在性,且在该凸性假设下建立了问题(VEP)关于近似拟全局真有效解的充分条件.最后,利用Tammer函数以及构建满足一定性质的非线性泛函,得到了问题(VEP)近似拟全局真有效解的标量化定理.
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收稿日期: 2020-04-08
PACS:O212.7
基金资助:国家自然科学基金(11861002),北方民族大学重大专项(ZDZX201804)资助项目.

引用本文:
韩文艳, 余国林. 非光滑向量均衡问题近似拟全局真有效解的最优性条件[J]. 应用数学学报, 2021, 44(1): 50-60. HAN Wenyan, YU Guolin. Optimality Conditions for Approximate Quasi Globally Proper Efficient Solutions to Nonsmooth Vector Equilibrium Problems. Acta Mathematicae Applicatae Sinica, 2021, 44(1): 50-60.
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