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1.
In this paper, the notion of the generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems are investigated.
By using the gap functions of the system of vector quasi-equilibrium problems, we establish the equivalent relationship between
the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems and that of the minimization problems.
We also present some metric characterizations for the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium
problems. The results in this paper are new and extend some known results in the literature. 相似文献
2.
In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-posedness by perturbations. We also show that under suitable conditions, the well-posedness by perturbations of a mixed variational inequality problem is equivalent to the well-posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution. 相似文献
3.
Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of continuous minimization problems coincide is given. It is shown that the equivalence between the original Tikhonov well-posedness and the ones above provides a new characterization of the so-called Atsuji spaces. Generalized notions of well-posedness, not requiring uniqueness of the solution, are introduced and investigated in the above spirit. 相似文献
4.
In this paper, the new notions of the generalized Tykhonov well-posedness for multiobjective generalized games are investigated.
By using the gap functions of the multiobjective generalized games, we establish the equivalent relationship between the generalized
Tykhonov well-posedness of the multiobjective generalized games and that of the minimization problems. Some metric characterizations
for the generalized Tykhonov well-posedness of the multiobjective generalized games are also presented. 相似文献
5.
G. P. Crespi M. Papalia M. Rocca 《Journal of Optimization Theory and Applications》2009,141(2):285-297
The notion of extended-well-posedness has been introduced by Zolezzi for scalar minimization problems and has been further
generalized to vector minimization problems by Huang. In this paper, we study the extended well-posedness properties of vector
minimization problems in which the objective function is C-quasiconvex. To achieve this task, we first study some stability properties of such problems.
Research partially supported by the Cariplo Foundation, Grant 2006.1601/11.0556, Cattaneo University, Castellanza, Italy. 相似文献
6.
B. S. Mordukhovich T. T. A. Nghia 《Journal of Optimization Theory and Applications》2012,155(3):762-784
The paper develops a new approach to the study of metric regularity and related well-posedness properties of convex set-valued mappings between general Banach spaces by reducing them to unconstrained minimization problems with objectives given as the difference of convex (DC) functions. In this way, we establish new formulas for calculating the exact regularity bound of closed and convex multifunctions and apply them to deriving explicit conditions ensuring well-posedness of infinite convex systems described by inequality and equality constraints. 相似文献
7.
In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational–hemivariational
inequalities with perturbations. We establish some metric characterizations for the well-posed variational–hemivariational
inequality and give some conditions under which the variational–hemivariational inequality is strongly well-posed in the generalized
sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational–hemivariational
inequality and the well-posedness of corresponding inclusion problem. 相似文献
8.
9.
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
10.
In this paper, well-posedness of generalized quasi-variational inclusion problems and of optimization problems with generalized quasi-variational inclusion problems as constraints is introduced and studied. Some metric characterizations of well-posedness for generalized quasi-variational inclusion problems and for optimization problems with generalized quasi-variational inclusion problems as constraints are given. The equivalence between the well-posedness of generalized quasi-variational inclusion problems and the existence of solutions of generalized quasi-variational inclusion problems is given under suitable conditions. 相似文献
11.
Well-posedness and convexity in vector optimization 总被引:9,自引:0,他引:9
We study a notion of well-posedness in vector optimization through the behaviour of minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We show that the notion of strict efficiency is related to the notion of well-posedness. Using the obtained results we identify a class of well-posed vector optimization problems: the convex problems with compact efficient frontiers. 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.
Levitin-Polyak well-posedness of variational inequalities 总被引:1,自引:0,他引:1
In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution. 相似文献
14.
Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed. 相似文献
15.
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
16.
M. Bianchi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):460-468
In this paper we introduce some notions of well-posedness for scalar equilibrium problems in complete metric spaces or in Banach spaces. As equilibrium problem is a common extension of optimization, saddle point and variational inequality problems, our definitions originates from the well-posedness concepts already introduced for these problems.We give sufficient conditions for two different kinds of well-posedness and show by means of counterexamples that these have no relationship in the general case. However, together with some additional assumptions, we show via Ekeland’s principle for bifunctions a link between them.Finally we discuss a parametric form of the equilibrium problem and introduce a well-posedness concept for it, which unifies the two different notions of well-posedness introduced in the first part. 相似文献
17.
Well-Posedness by Perturbations of Variational Problems 总被引:3,自引:0,他引:3
Lemaire B. Ould Ahmed Salem C. Revalski J. P. 《Journal of Optimization Theory and Applications》2002,115(2):345-368
In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented. 相似文献
18.
Rong Hu Ying-Kang Liu Ya-Ping Fang 《Journal of Fixed Point Theory and Applications》2017,19(4):2209-2223
In this paper, we extend well-posedness notions to the split minimization problem which entails finding a solution of one minimization problem such that its image under a given bounded linear transformation is a solution of another minimization problem. We prove that the split minimization problem in the setting of finite-dimensional spaces is Levitin–Polyak well-posed by perturbations provided that its solution set is nonempty and bounded. We also extend well-posedness notions to the split inclusion problem. We show that the well-posedness of the split convex minimization problem is equivalent to the well-posedness of the equivalent split inclusion problem. 相似文献
19.
20.
We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces. 相似文献