黎曼流形上弱向量似变分不等式解的存在性
Existence of Solutions to Weak Vector Variational-Like Inequalities on Riemannian Manifolds
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摘要: 在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念.研究这类弱向量似变分不等式和向量优化问题弱有效解之间的关系.利用最大元定理证明了弱向量变分不等式解的存在性,并给出了向量优化问题弱有效解存在的条件.Abstract: The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented. The relationship between this kind of weak vector variation-like inequalities and the weak efficient solution of vector optimization problems is obtained. By using the maximum element theorem, the existence theorem for weak vector variational-like inequalities defined on Riemannian manifolds is given. Moreover, the conditions for the existence of weak efficient solution to vector optimization problems are presented.
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