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1.
本文利用例外簇方法研究非强制混合向量变分不等式的弱有效解的存在性:首先证明若混合向量变分不等式问题不存在例外簇,则混合向量变分不等式问题的弱有效解集为非空集合:利用向量值映射的渐近映射给出自反Banach空间中非强制混合向量变分不等式的弱有效解集不存在例外簇的充分条件,从而得到混合向量变分不等式问题的弱有效解的存在性结果;我们研究了当算子为余正仿射算子时,给出混合仿射向量变分不等式不存在例外簇的充分条件,得到混合仿射向量变分不等式弱有效解的存在性,给出了混合仿射向量变分不等式的弱有效解集为非空紧致集的充分条件.将Iusem等人(2019)在有限维空间中标量混合变分不等式解的存在性结果推广到自反Banach空间中混合向量变分不等式. 相似文献
2.
In this paper we study the feasibility and solvability of vector variational inequalities with moving cones in Banach spaces. We show that the strict feasibility implies solvability of vector variational inequalities with moving cones under suitable conditions. Further we show that under suitable conditions, the homogeneous vector variational inequality with a moving cone is solvable whenever it is feasible. As consequences, we obtain the solvability of vector variational inequalities with feasibility assumptions in Banach spaces. 相似文献
3.
《Optimization》2012,61(2):167-180
This article introduces a new concept of an exceptional family of elements for a generalized set-valued variational inequality in Banach spaces. By using this concept and the degree theory for the generalized set-valued variational inequality introduced by Wang and Huang [Zh.B. Wang and N.J. Huang, Degree theory for a generalized set-valued variational inequality with an application in Banach spaces, J. Glob. Optim. 49 (2011), pp. 343–357], some solvability results for the generalized set-valued variational inequality and its special cases are given in Banach spaces under suitable conditions. 相似文献
4.
5.
Jinlu Li 《Optimization》2018,67(5):565-583
In this paper, we introduce the concept of isotone cones in Banach spaces. Then, we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity conditions in partially ordered Banach spaces. 相似文献
6.
Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem 总被引:6,自引:0,他引:6
The concepts of monotone pair of mappings and vector implicit complementarity problem (VICP) in ordered Banach spaces are introduced. Existence theorems for simultaneous vector variational inequalities (VVI) and VICP are proved. 相似文献
7.
L. C. Ceng B. S. Mordukhovich J. C. Yao 《Journal of Optimization Theory and Applications》2010,146(2):267-303
This paper studies a general vector optimization problem of finding weakly efficient points for mappings from Hilbert spaces
to arbitrary Banach spaces, where the latter are partially ordered by some closed, convex, and pointed cones with nonempty
interiors. To find solutions of this vector optimization problem, we introduce an auxiliary variational inequality problem
for a monotone and Lipschitz continuous mapping. The approximate proximal method in vector optimization is extended to develop
a hybrid approximate proximal method for the general vector optimization problem under consideration by combining an extragradient
method to find a solution of the variational inequality problem and an approximate proximal point method for finding a root
of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate
solutions to the variational inequality problem for monotone and Lipschitz continuous mapping, and then finding weakly efficient
points for a suitable regularization of the original mapping. We present both absolute and relative versions of our hybrid
algorithm in which the subproblems are solved only approximately. The weak convergence of the generated sequence to a weak
efficient point is established under quite mild assumptions. In addition, we develop some extensions of our hybrid algorithms
for vector optimization by using Bregman-type functions. 相似文献
8.
On Vector Variational Inequalities in Reflexive Banach Spaces 总被引:5,自引:0,他引:5
In this paper, we study the solvability for a class of vector variational inequalities in reflexive Banach spaces. By using
Brouwer fixed point theorem, we prove the solvability for this class of vector variational inequalities without monotonicity
assumption. The solvability results for this class of vector variational inequalities with monotone mappings are also presented
by using the KKM-Fan lemma
This paper is dedicated to Professor Franco Giannessi for his 68th birthday 相似文献
9.
In this paper, a general system of nonlinear variational inequality problem in Banach spaces was considered, which includes some existing problems as special cases. For solving this nonlinear variational inequality problem, we construct two methods which were inspired and motivated by Korpelevich’s extragradient method. Furthermore, we prove that the suggested algorithms converge strongly to some solutions of the studied variational inequality. 相似文献
10.
In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc. 相似文献
11.
在Banach空间中,引入和研究了新的广义H-η-增生算子,对广义m-增生算子与H-η-单调算子提供了一个统一的框架.还定义了广义H-η-增生算子相应的预解算子,并且证明了其Lipschitz连续性.作为应用,考虑了涉及广义H-η-增生算子的一类变分包含问题的可解性.利用预解算子方法,构造了一个求解变分包含的迭代算法.在适当假设下,证明了变分包含解的存在性和由算法生成的迭代序列的收敛性. 相似文献
12.
Habtu Zegeye 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(1):263-272
We introduce an iterative process for finding an element in the common fixed point set of finite family of closed relatively quasi-nonexpansive mappings, common solutions of finite family of equilibrium problems and common solutions of finite family of variational inequality problems for monotone mappings in Banach spaces. Our theorem extends and unifies most of the results that have been proved for this important class of nonlinear operators. 相似文献
13.
Mark Krasnosel'skii Reinhard Mennicken Dmitrii Rachinskii 《Mathematische Nachrichten》1997,188(1):203-218
New conditions are suggested for the existence of solutions of two-point boundary -value problems. The situation is studied when monotone bounds of nonlinear terms do not guarantee the solvability of the problems. The approach developed is a combination of variational methods, simple fixed point principles, and methods of partially ordered spaces. 相似文献
14.
By employing the notion of exceptional family of elements, we establish some existence results for generalized variational
inequality problems in reflexive Banach spaces provided that the mapping is upper sign-continuous. We show that the nonexistence
of an exceptional family of elements is a necessary condition for the solvability of the dual variational inequality. For
quasimonotone variational inequalities, we present some sufficient conditions for the existence of strong solutions. For the
pseudomonotone case, the nonexistence of an exceptional family of elements is proved to be an equivalent characterization
of the problem having strong solutions. Furthermore, we establish several equivalent conditions for the solvability for the
pseudomonotone case. As a byproduct, a quasimonotone generalized variational inequality is proved to have a strong solution
if it is strictly feasible. Moreover, for the pseudomonotone case, the strong solution set is nonempty and bounded if it is
strictly feasible. 相似文献
15.
In this paper, we establish the equivalence between the existence of zeros for set-valued mappings and the solvability of variational inequality, under some conditions involving the generalized projection operator. Basing on this result, we obtain some existence theorems of zeros for quasimonotone set-valued mappings. As application, we derive several fixed point theorems for generalized inward mappings in Hilbert spaces. 相似文献
16.
Kamal N. Soltanov 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):164-175
Here we consider perturbations of continuous mappings on Banach spaces, and investigate their images under various conditions. Consequently we study the solvability of some classes of equations and inclusions. For these we start by the investigation of local properties of the considered mapping and local comparisons of this mapping with certain smooth mappings. Moreover, we study different mixed problems. 相似文献
17.
In this paper, we first introduce the concept of Levitin-Polyak well-posedness of a generalized mixed variational inequality in Banach spaces and establish some characterizations of its Levitin-Polyak well-posedness. Under suitable conditions, we prove that the Levitin-Polyak well-posedness of a generalized mixed variational inequality is equivalent to the Levitin-Polyak well-posedness of a corresponding inclusion problem and a corresponding fixed point problem. We also derive some conditions under which a generalized mixed variational inequality in Banach spaces is Levitin-Polyak well-posed. 相似文献
18.
该文在半序锥度量空间中研究了有关三个映射的公共不动点的存在唯一性,不要求映射的连续性和交换性,也不要求锥的正规性,其结果改进并推广了文献中的一些重要结论. 相似文献
19.
Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations 总被引:1,自引:0,他引:1
We prove some fixed point theorems in partially ordered sets, providing an extension of the
Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider
in this paper nonincreasing mappings as well as non monotone mappings. We also present some
applications to first–order ordinary differential equations with periodic boundary conditions, proving
the existence of a unique solution admitting the existence of a lower solution.
Research partially supported by Ministerio de Educación y Ciencia and FEDER, Project MTM2004-06652-C03-01, and by Xunta de
Galicia and FEDER, Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN 相似文献
20.
Monotone generalized variational inequalities and generalized complementarity problems 总被引:1,自引:0,他引:1
Some existence results for generalized variational inequalities and generalized complementarity problems involving quasimonotone and pseudomonotone set-valued mappings in reflexive Banach spaces are proved. In particular, some known results for nonlinear variational inequalities and complementarity problems in finite-dimensional and infinite-dimensional Hilbert spaces are generalized to quasimonotone and pseudomonotone set-valued mappings and reflexive Banach spaces. Application to a class of generalized nonlinear complementarity problems studied as mathematical models for mechanical problems is given.The research of the first author was supported by the National Natural Science Foundation of P. R. China and by the Ethel Raybould Fellowship, University of Queensland, St. Lucia, Brisbane, Australia. 相似文献