共查询到19条相似文献,搜索用时 93 毫秒
1.
向量似变分不等式解的存在性及解集的稳定性 总被引:3,自引:0,他引:3
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. 相似文献
2.
广义向量似变分不等式解集的通有稳定性及本质连通区的存在性 总被引:10,自引:0,他引:10
本文研究广义向量似变分不等式解集的稳定性.证明了在满足一定的连续性和凸 性条件的广义向量似变分不等式问题构成的空间M中,大多数(在Baire分类意下)广 义向量似变分不等式问题的解集是稳定的,并证明了M中的每个广义向量似变分不等式 的解集至少存在一个本质连通区。 相似文献
3.
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. 相似文献
4.
拟变分不等式解集的极小本质集及应用 总被引:1,自引:0,他引:1
引入了拟变分不等式解集的极小本质集的概念,并证明了每个拟变分不等式(满足一定条件)的解集至少存在一个极小本质集.作为应用,还证明了大多数(在Baire分类意义下)拟-似变分不等式问题的解集是稳定的;每个拟-似变分不等式(满足一定条件)的解集至少存在一个本质连通区. 相似文献
5.
黄龙光 《纯粹数学与应用数学》2001,17(4):314-317
研究拓扑向量空间半准内凸函数的特性,给出半内凸弧方向可微函数的最小值可由一类似变分不等式问题的解表示及一类广义变分不等式解的唯一性。 相似文献
6.
研究拓扑向量空间上弱广义向量拟似变分不等式解的存在性问题.与Khaliq和Rashid等在单调或伪单调假设条件下,利用KKM定理证明解的存在性不同,在集值映射是非空凸值映射并且有开下截口的条件下,利用Fan-Browder不动点原理证明解的存在性. 相似文献
7.
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. 相似文献
8.
广义集值强非线性混合似变分不等式解的迭代逼近 总被引:4,自引:0,他引:4
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. 相似文献
9.
广义混合似变分不等式组的两步迭代算法 总被引:1,自引:0,他引:1
对H ilbert空间中一类广义混合似变分不等式组进行了研究;利用次微分算子的预解式技术,建立了广义混合似变分不等式组与不动点问题之间的等价关系;给出了一个求解这种广义混合似变分不等式组的显式两步迭代算法;并证明了该算法在适当的条件下收敛. 相似文献
10.
研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
11.
M. Golestani H. Sadeghi Y. Tavan 《Journal of Optimization Theory and Applications》2018,179(3):896-916
In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn–Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved. 相似文献
12.
Qamrul Hasan Ansari Mahboubeh Rezaie Jafar Zafarani 《Journal of Global Optimization》2012,53(2):271-284
In this paper, we consider different kinds of generalized vector variational-like inequality problems and a vector optimization problem. We establish some relationships between the solutions of generalized Minty vector variational-like inequality problem and an efficient solution of a vector optimization problem. We define a perturbed generalized Stampacchia vector variational-like inequality problem and discuss its relation with generalized weak Minty vector variational-like inequality problem. We establish some existence results for solutions of our generalized vector variational-like inequality problems. 相似文献
13.
In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan’s main results are corrected. 相似文献
14.
In this paper, we study the relationship among the generalized Minty vector variational-like inequality problem, generalized
Stampacchia vector variational-like inequality problem and vector optimization problem for nondifferentiable and nonconvex
functions. We also consider the weak formulations of the generalized Minty vector variational-like inequality problem and
generalized Stampacchia vector variational-like inequality problem and give some relationships between the solutions of these
problems and a weak efficient solution of the vector optimization problem. 相似文献
15.
In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps and obtain an explicit expression of its contingent derivative. We also establish some necessary optimality conditions for solutions of the generalized weak vector variational inequality, which generalize the corresponding results in the literature. Furthermore, we establish some unified necessary and sufficient optimality conditions for local optimal solutions of the generalized weak vector variational inequality. Simultaneously, we also show that there is no gap between the necessary and sufficient conditions under an appropriate condition. 相似文献
16.
In this paper, we introduce and study a class of generalized nonlinear vector variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems and so on. Applying maximal element theorem, we prove the existence of its solutions in the setting of locally convex topological vector space. 相似文献
17.
In a recent paper, Domokos and Kolumbán introduced variational inequalities with operator solutions to provide a suitable
unified approach to several kinds of variational inequality and vector variational inequality in Banach spaces. Inspired by
their work, in this paper, we further develop the new scheme of vector variational inequalities with operator solutions from
the single-valued case into the multi-valued one. We prove the existence of solutions of generalized vector variational inequalities
with operator solutions and generalized quasi-vector variational inequalities with operator solutions. Some applications to
generalized vector variational inequalities and generalized quasi-vector variational inequalities in a normed space are also
provided. 相似文献
18.
In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given. 相似文献
19.
介绍了广义集值隐向量变分不等式问题系统,并且通过Kakutani-Fan-Glicksberg不动点定理,建立了其解的存在性结果;在此基础上,研究了广义集值隐向量变分不等式问题系统的稳定性,建立了其解集本质连通区的存在性结果. 相似文献