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1.
In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results,
we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems
of variational inclusion constraints, bilevel problem with systems of constraints. 相似文献
2.
Lai-Jiu Lin 《Journal of Global Optimization》2007,38(1):21-39
In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result,
we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium
problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical
program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and
systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints.
This research was supported by the National Science Council of the Republic of China. 相似文献
3.
Lai-Jiu Lin 《Journal of Global Optimization》2007,39(4):509-527
In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence
results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point,
existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and
vector mathematical programs with variational inclusions constraints. 相似文献
4.
Lai-Jiu Lin 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):37-49
In this paper, we study systems of quasi-variational inclusion problem and systems of quasi-variational disclusion problem. From the existence theorems of solution for these two types of problems, we study various types of systems of quasi-variational inclusion problems, systems of quasi-equilibrium problems, systems of quasi-KKM theorem, abstract economics and system of KKM theorem. We also show their equivalent relations. We study further existence theorems of solution for generalized quasi-variational inclusion problem. Our results are different from any existence result in the literature. 相似文献
5.
丁协平 《数学物理学报(B辑英文版)》2011,31(3):1142-1154
In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces. 相似文献
6.
Lai-Jiu Lin 《Journal of Global Optimization》2007,37(2):275-286
In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program
with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program
with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We
establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions. 相似文献
7.
In this paper, we establish existence theorems of quasivariational inclusion problems; from them, we establish existence theorems
of mathematical programs with quasivariational inclusion constraint, bilevel problems, mathematical programs with equilibrium
constraint and semi-infinite problems.
This research was supported by the National Science Council of the Republic of China. The authors express their gradtitude
to the referees for valuable suggestions. 相似文献
8.
Wei-Shih Du 《Journal of Global Optimization》2010,47(1):119-132
In this paper, we first establish the existence theorems of the solution of hybrid inclusion and disclusion systems, from
which we study mixed types of systems of generalized quasivariational inclusion and disclusion problems and systems of generalized
vector quasiequilibrium problems. Some applications of existence theorems to feasible points for various mathematical programs
with variational constraints or equilibrium constraints, system of vector saddle point and system of minimax theorem are also
given. 相似文献
9.
L. J. Lin 《Journal of Optimization Theory and Applications》2008,137(1):27-40
In this paper, we establish existence theorems for bilevel problems with fixed-point constraints and bilevel problems without
fixed-point constraint. The aim of this paper is to investigate under which conditions the existence of a feasible point of
a bilevel problem can be assumed in advance and under which conditions there exist minimizers for this type of problems. From
this, we establish existence theorems for mathematical programs with equilibrium constraints and semi-infinite problems.
This research was supported by the National Science Council of the Republic of China. The author thanks the referees for suggestions
and comments leading to the present form of the paper. 相似文献
10.
Y. C. Liou X. Q. Yang J. C. Yao 《Journal of Optimization Theory and Applications》2005,126(2):345-355
In this paper, we introduce mathematical programs with vector optimization constraints. For these problems, we establish two models in both the weak Pareto solution and Pareto solution setting. Some new existence results are obtained under rather weak conditions. We establish also equivalences between mathematical programs with vector optimization constraints and mathematical programs with vector variational inequality constraints.This research was partially supported by a grant from the National Science Council of the ROC. The authors thank the referees for helpful suggestions and comments. 相似文献
11.
Chih-Sheng Chuang 《Optimization》2016,65(4):811-825
In this paper, we study the well-posedness for the parametric optimization problems with variational inclusion problems as constraint (or the perturbed problem of optimization problems with constraint). Furthermore, we consider the relation between the well-posedness for the parametric optimization problems with variational inclusion problems as constraint and the well-posedness in the generalized sense for variational inclusion problems. 相似文献
12.
In this paper, we introduce systems of vector quasi-equilibrium problems and prove the existence of their solutions. As applications
of our results, we derive the existence theorems for solution of system of vector quasi-saddle point problem, the existences
theorems of a solution of system of generalized quasi-minimax inequalities, the mathematical program with equilibrium constraint,
semi-infinite and bilevel problems. 相似文献
13.
This paper focuses on the single-level reformulation of mixed integer bilevel programming problems (MIBLPP). Due to the existence of lower-level integer variables, the popular approaches in the literature such as the first-order approach are not applicable to the MIBLPP. In this paper, we reformulate the MIBLPP as a mixed integer mathematical program with complementarity constraints (MIMPCC) by separating the lower-level continuous and integer variables. In particular, we show that global and local minimizers of the MIBLPP correspond to those of the MIMPCC respectively under suitable conditions. 相似文献
14.
In this paper, we apply an existence theorem for the variational inclusion problem to study the existence results for the variational intersection problems in Ekeland’s sense and the existence results for some variants of set-valued vector Ekeland variational principles in a complete metric space. Our results contain Ekeland’s variational principle as a special case and our approaches are different to those for any existence theorems for such problems. 相似文献
15.
Lai-Jiu Lin Chih-Sheng Chuang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):651-661
In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces. 相似文献
16.
We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers. 相似文献
17.
18.
Chih-Sheng Chuang 《Optimization》2016,65(4):859-876
Split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present feasible algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for these algorithms. As application, we study the split feasibility problem in real Hilbert spaces. Final, numerical results are given for our main results. 相似文献
19.
In this paper, we study the well-posedness in the generalized sense for variational inclusion problems and variational disclusion problems, the well-posedness for optimization problems with variational inclusion problems, variational disclusion problems and scalar equilibrium problems as constraint. 相似文献
20.
The studies of systems of variational inclusions problems and variational disclusions problems with applications 总被引:1,自引:0,他引:1
In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems. 相似文献