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1.
Marius Durea Radu Strugariu Christiane Tammer 《Journal of Optimization Theory and Applications》2017,175(3):738-763
The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new. 相似文献
2.
In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings. 相似文献
3.
In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given. 相似文献
4.
The aim of this note is to get new results concerning set-valued vector equilibrium problems, which extend some recent assertions in this field. 相似文献
5.
M. Durea 《Journal of Mathematical Analysis and Applications》2008,348(2):589-606
The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well. 相似文献
6.
Scalarization for pointwise well-posed vectorial problems 总被引:1,自引:1,他引:0
M. Durea 《Mathematical Methods of Operations Research》2007,66(3):409-418
The aim of this paper is to develop a method of study of Tykhonov well-posedness notions for vector valued problems using
a class of scalar problems. Having a vectorial problem, the scalarization technique we use allows us to construct a class
of scalar problems whose well-posedness properties are equivalent with the most known well-posedness properties of the original
problem. Then a well-posedness property of a quasiconvex level-closed problem is derived.
相似文献
7.
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties to deduce implicit theorems for set-valued maps. Finally, we present some applications to the study of multicriteria optimization problems. 相似文献
8.
Marius Durea Van Ngai Huynh Huu Tron Nguyen Radu Strugariu 《Journal of Mathematical Analysis and Applications》2014
The paper concerns a new method to obtain a proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years in the literature. In turn, these techniques are based on several important concepts (like error bounds, lower semicontinuous envelope of a set-valued map, local composition stability of multifunctions) and allow us to obtain two new proofs of a recent result having deep roots in the topic of regularity of mappings. Moreover, we make clear the idea that it is possible to use (co)derivative conditions as tools of proof for openness results in very general situations. 相似文献
9.
M. Durea 《Journal of Global Optimization》2010,47(1):13-27
The aim of this paper is to study optimality conditions for strict local minima to constrained mathematical problems governed
by scalar and vectorial mappings. Unlike other papers in literature dealing with strict efficiency, we work here with mappings
defined on infinite dimensional normed vector spaces. Firstly, we (mainly) consider the case of nonsmooth scalar mappings
and we use the Fréchet and Mordukhovich subdifferentials in order to provide optimality conditions. Secondly, we present some
methods to reduce the study of strict vectorial minima to the case of strict scalar minima by means of some scalarization
techniques. In this vectorial framework we treat separately the case where the ordering cone has non-empty interior and the
case where it has empty interior. 相似文献
10.