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1.
In this paper, we aim to suggest the new concept of well-posedness for the general parametric quasi-variational inclusion problems (QVIP). The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for QVIP. Some metric characterizations of well-posedness for QVIP are given. We prove that under suitable conditions, the well-posedness is equivalent to the existence of uniqueness of solutions. As applications, we obtain immediately some results of well-posedness for the parametric quasi-variational inclusion problems, parametric vector quasi-equilibrium problems and parametric quasi-equilibrium problems. 相似文献
2.
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
3.
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
4.
《Optimization》2012,61(7):997-1011
In this article, the concepts of well-posedness and well-posedness in the generalized sense are introduced for parametric quasivariational inequality problems with set-valued maps. Metric characterizations of well-posedness and well-posedness in the generalized sense, in terms of the approximate solutions sets, are presented. Characterization of well-posedness under certain compactness assumptions and sufficient conditions for generalized well-posedness in terms of boundedness of approximate solutions sets are derived. The study is further extended to discuss well-posedness for an optimization problem with quasivariational inequality constraints. 相似文献
5.
In this paper, three kinds of well-posedness for set optimization are first introduced. By virtue of a generalized Gerstewitz’s function, the equivalent relations between the three kinds of well-posedness and the well-posedness of three kinds of scalar optimization problems are established, respectively. Then, sufficient and necessary conditions of well-posedness for set optimization problems are obtained by using a generalized forcing function, respectively. Finally, various criteria and characterizations of well-posedness are given for set optimization problems. 相似文献
6.
Lai-Jiu Lin Qamrul Hasan Ansari Yu-Jen Huang 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper, we consider systems of vector quasi-variational inclusions which include systems of vector quasi-equilibrium problems for multivalued maps, systems of vector optimization problems and several other systems as special cases. We establish existence results for solutions of these systems. As applications of our results, we derive the existence results for solutions of system vector optimization problems, mathematical programs with systems of vector variational inclusion constraints and bilevel problems. Another application of our results provides the common fixed point theorem for a family of lower semicontinuous multivalued maps. Further applications of our results for existence of solutions of systems of vector quasi-variational inclusions are given to prove the existence of solutions of systems of Minty type and Stampacchia type generalized implicit quasi-variational inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature. 相似文献
7.
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
8.
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
9.
In this paper, we consider Levitin–Polyak well-posedness of parametric generalized equilibrium problems and optimization problems
with generalized equilibrium constraints. Some criteria for these types of well-posedness are derived. In particular, under
certain conditions, we show that generalized Levitin–Polyak well-posedness of a parametric generalized equilibrium problem
is equivalent to the nonemptiness and compactness of its solution set. Finally, for an optimization problem with generalized
equilibrium constraints, we also obtain that, under certain conditions, Levitin–Polyak well-posedness in the generalized sense
is equivalent to the nonemptiness and compactness of its solution set. 相似文献
10.
In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given. 相似文献
11.
《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4585-4603
We introduced and studied the concept of well-posedness to a generalized mixed variational inequality. Some characterizations are given. Under suitable conditions, we prove that the well-posedness of the generalized mixed variational inequality is equivalent to the well-posedness of the corresponding inclusion problem. We also discuss the relations between the well-posedness of the generalized mixed variational inequality and the well-posedness of the corresponding fixed-point problem. Finally, we derive some conditions under which the generalized mixed variational inequality is well-posed. 相似文献
12.
Extended well-posedness of optimization problems 总被引:8,自引:0,他引:8
T. Zolezzi 《Journal of Optimization Theory and Applications》1996,91(1):257-266
The well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended well-posedness. It is shown that this new property can be characterized by metric criteria, which parallel to some extent those known about generalized Tikhonov well-posedness.This work was partially supported by MURST, Fondi 40%, Rome, Italy. 相似文献
13.
X. X. Huang 《Mathematical Methods of Operations Research》2001,53(1):101-116
14.
W.Y. Zhang 《Journal of Mathematical Analysis and Applications》2012,387(2):909-915
In this paper, the notion of a generalized Levitin–Polyak well-posedness is defined for symmetric vector quasi-equilibrium problems. Sufficient conditions are given for the generalized Levitin–Polyak well-posedness. Moreover, it is shown that the results can be refined in the convex case. 相似文献
15.
In this paper, we introduce several types of Levitin-Polyak well-posedness for a generalized vector quasi-equilibrium problem
with functional constraints and abstract set constraints. Criteria and characterizations of these types of Levitin-Polyak
well-posedness with or without gap functions of generalized vector quasi-equilibrium problem are given. The results in this
paper unify, generalize and extend some known results in the literature. 相似文献
16.
In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem. 相似文献
17.
In this paper, we consider the vector equilibrium problems involving lexicographic cone in Banach spaces. We introduce the new concepts of the Tykhonov well-posedness for such problems. The corresponding concepts of the Tykhonov well-posedness in the generalized sense are also proposed and studied. Some metric characterizations of well-posedness for such problems are given. As an application of the main results, several results on well-posedness for the class of lexicographic variational inequalities are derived. 相似文献
18.
19.
In this paper, we first derive several characterizations of the nonemptiness and compactness for the solution set of a convex scalar set-valued optimization problem (with or without cone constraints) in which the decision space is finite-dimensional. The characterizations are expressed in terms of the coercivity of some scalar set-valued maps and the well-posedness of the set-valued optimization problem, respectively. Then we investigate characterizations of the nonemptiness and compactness for the weakly efficient solution set of a convex vector set-valued optimization problem (with or without cone constraints) in which the objective space is a normed space ordered by a nontrivial, closed and convex cone with nonempty interior and the decision space is finite-dimensional. We establish that the nonemptiness and compactness for the weakly efficient solution set of a convex vector set-valued optimization problem (with or without cone constraints) can be exactly characterized as those of a family of linearly scalarized convex set-valued optimization problems and the well-posedness of the original problem. 相似文献
20.
研究了Banach空间中一类广义集值拟变分包含问题的灵敏性分析.利用预解算子的技巧,在对给定条件没有假设可微性和单调性下,建立了这类问题与广义预解方程类的等价性. 相似文献