Vector optimization and variational-like inequalities

In this paper, some properties of pseudoinvex functions are obtained. We study the equivalence between different solutions of the vector variational-like inequality problem. Some relations between vector variational-like inequalities and vector optimization problems for non-differentiable functions under generalized monotonicity are established. J. Zafarani was partially supported by the Center of Excellence for Mathematics (University of Isfahan).     

Generalized vector variational-like inequalities and vector optimization in Asplund spaces

Some properties of pseudoinvex functions, defined by means of limiting subdifferential, are obtained. Furthermore, the equivalence between vector variational-like inequalities involving limiting subdifferential and vector optimization problems are studied under pseudoinvexity condition.     

广义集值强非线性混合似变分不等式解的迭代逼近

延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式．证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性．利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法,最终证明了这类广义强非线性混合似变分不等式解的存在性及由算法生成的迭代序列的收敛性．     

广义集值强非线性混合似变分不等式解的迭代逼近

辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.     

自反Banach空间内混合非线性似变分不等式解的算法*

本文在自反Banach空间内研究了一类混合非线性似变分不等式应用作者得到的一个极小极大不等式,对这类混合非线性似变分不等式的解,证明了几个存在唯一性定理其次由应用辅助问题技巧,作者建议了一个计算此类混合非线性似变分不等式的近似解的创新算法最后讨论收敛性准则.     

广义Minty 向量似变分不等式解的性质

在拓扑向量空间中讨论下Dini方向导数形式的广义Minty向量似变分不等式问题. 可微形式的Minty变分不等式、Minty似变分不等式和Minty向量变分不等式是其特殊形式. 该文分别讨论了Minty向量似变分不等式的解与径向递减函数, 与向量优化问题的最优解或有效解之间的关系问题, 以及Minty向量似变分不等式的解集的仿射性质. 这些定理推广了文献中Minty变分不等式的一些重要的已知结果.     

自反Banach空间中广义混合双线性变分不等式解的存在性

介绍了自反B anach空间中一类广义混合双线性型变分不等式,利用极大极小不等式和辅助变分原理技术证明了这类混合双线性型变分不等式解的存在性与唯一性.     

On equilibrium-like problems

In this article we introduce a new class of equilibrium problems known as mixed quasi invex equilibrium (equilibrium-like) problems with trifunction. This class of equilibrium problems includes invex equilibrium problems, variational inequalities and variational-like inequalities as special cases. We use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under mild conditions. Our results represent significant and important refinements of the previously known results.     

Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings

In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces.     

向量似变分不等式解的存在性及解集的稳定性

本文首先得到一类广义向量似变分不等式问题的解的存在性定理,然后利用usco映射的性质,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数(在Baire分类意义下)广义向量似变分不等式问题的解集是稳定的;另外还引入广义向量似变分不等式解集的本质连通区的概念,并证明了满足一定连续性、凸性条件的广义向量似变分不等式的解集至少存在一个本质连通区.