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1.
Convergence properties of convolutions, conjugations, compositions and polarities are expressed in terms of inequalities involving Γ-operators and generalized extremal convolutions. It is shown that Γ-inequalities amount to simple algebraic inequalities and (in some cases) to some min-max problems. Numerous applications are indicated, in particular, to continuity properties of the classical conjugation. 相似文献
2.
In this note, we prove that the convergence results for vector optimization problems with equilibrium constraints presented
in Wu and Cheng (J. Optim. Theory Appl. 125, 453–472, 2005) are not correct. Actually, we show that results of this type cannot be established at all. This is due to the possible lack,
even under nice assumptions, of lower convergence of the solution map for equilibrium problems, already deeply investigated
in Loridan and Morgan (Optimization 20, 819–836, 1989) and Lignola and Morgan (J. Optim. Theory Appl. 93, 575–596, 1997). 相似文献
3.
Topological existence and stability for stackelberg problems 总被引:1,自引:0,他引:1
The aim of this paper is to study, in a topological framework, existence and stability for the solutions to a parametrized Stackelberg problem. To this end, approximate solutions are used, more precisely, -solutions and strict -solutions. The results given are of minimal character and the standard types of constraints are considered, that is, constant constraints, constraints defined by a finite number of inequalities, and more generally constraints defined by an arbitrary multifunction. 相似文献
4.
α-Well-posedness for Nash Equilibria and For Optimization Problems with Nash Equilibrium Constraints
We present the concepts of α-well-posedness for parametric noncooperative games and for optimization problems with constraints defined by parametric Nash equilibria. We investigate some classes of functions that ensure these types of well-posedness and the connections with α-well-posedness for variational inequalities and optimization problems with variational inequality constraints. 相似文献
5.
M.B. Lignola 《Operations Research Letters》2008,36(6):710-714
We consider variational problems in Banach spaces. Well-posedness concepts for such problems are introduced and investigated by means of two gap functions and their Moreau-Yosida regularizations. 相似文献
6.
M. Beatrice Lignola Jacqueline Morgan 《Computational Optimization and Applications》2012,53(2):485-503
In general the infimal value of a mathematical program with variational inequality constraints (MPVI) is not stable under perturbations in the sense that the sequence of infimal values for the perturbed programs may not converge to the infimal value of the original problem even in presence of nice data. Thus, for these programs we consider different types of values which approximate the exact value from below or/and from above under or without perturbations. 相似文献
7.
In this paper, a Ky Fan inequality without compactness and semicontinuity assumptions is proved. The inequality is next applied in order to obtain existence results for Nash equilibrium points for two-person games in topological vector spaces and in reflexive Banach spaces. 相似文献
8.
Stability of Regularized Bilevel Programming Problems 总被引:2,自引:0,他引:2
A bilevel programming problem S is considered. First, sufficient conditions of minimal character are given on the data of the problem in order to guarantee the lower semicontinuity of the marginal function of the upper level problem. Then, for >0, a regularized problem S() is considered for which continuity of the regularized marginal function and convergence of the approximate value, as goes to zero, are obtained. Moreover, under perturbations on the data, convergence results for the perturbed marginal functions and the solutions to the problem S
n() are given for any >0. 相似文献
9.
MinSup problems with constraints described by quasi-equilibrium problems are considered in Banach spaces. The solutions set of such problems may be empty even in very good situations, so the aim of this paper is twofold. First, we determine appropriate regularizations (called inner regularizations) which allow to reach the value of the original problem. Then, among these regularizations we identify those which allow to bypass the lack of exact solutions to these problems by a suitable concept of “viscosity” solution whose existence is then proved under reasonable assumptions. 相似文献
10.
Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems 总被引:1,自引:0,他引:1
M. Beatrice Lignola Jacqueline Morgan 《Journal of Optimization Theory and Applications》2017,173(1):183-202
Pessimistic bilevel optimization problems are not guaranteed to have a solution even when restricted classes of data are involved. Thus, we propose a concept of viscosity solution, which satisfactorily obviates the lack of optimal solutions since it allows to achieve in appropriate conditions the security value. Differently from the viscosity solution concept for optimization problems, introduced by Attouch (SIAM J Optim 6:769–806, 1996) and defined through a viscosity function that aims at regularizing the objective function, viscosity solutions for pessimistic bilevel optimization problems are defined through regularization families of the solutions map to the lower-level optimization. These families are termed “inner regularizations” since they approach the optimal solutions map from the inside. First, we investigate, in Banach spaces, several classical regularizations of parametric constrained minimum problems giving sufficient conditions for getting inner regularizations; then, we establish existence results for the corresponding viscosity solutions under possibly discontinuous data. 相似文献