arXiv subjects

Radu Strugariu

Publications and source records attributed to Radu Strugariu.

8 recordsLinked to original sources

arXiv2026

Bishop-Phelps Type Scalarization for Vector Optimization in Real Topological-Linear Spaces

It is well-known that scalarization techniques (e.g., in the sense of Gerstewitz; Kasimbeyli; Pascoletti and Serafini; Zaffaroni) are useful for generating (weakly, properly) efficient solutions of vector optimization problems. One recognized approach is the conic scalarization method in vector optimization in real normed spaces proposed by Kasimbeyli (2010, SIAM J Optim 20), which is based on augmented dual cones and Bishop-Phelps type (norm-linear) scalarizing functions. In this paper, we present new results on cone separation in real topological-linear spaces by using Bishop-Phelps type separating cones / separating seminorm-linear functions. Moreover, we study some extensions of known scalarization results in vector optimization (in the sense of Eichfelder; Gerstewitz; Jahn; Kasimbeyli; Pascoletti and Serafini). On this basis, we propose a Bishop-Phelps type scalarization method for vector optimization problems in real topological-linear spaces, which is based on Bishop-Phelps type cone-representing and cone-monotone scalarizing functions (e.g., Gerstewitz scalarizing functions or seminorm-linear scalarizing functions). Thus, our method also extends Kasimbeyli's conic scalarization method from real normed spaces to real topological-linear spaces. Within this framework, we derive new Bishop-Phelps type scalarization results for the concepts of weak efficiency and different types of proper efficiency.

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arXiv2025

Necessary conditions for approximate solutions of vector and set optimization problems with variable domination structure

We consider vector and set optimization problems with respect to variable domination structures given by set-valued mappings acting between the preimage space and the image space of the objective mapping, as well as by set-valued mappings with the same input and output space, that coincides with the image space of the objective mapping. The aim of this paper is to derive necessary conditions for approximately nondominated points of problems with a single-valued objective function, employing an extension of Ekeland's Variational Principle for problems with respect to variable domination structures in terms of generalized differentiation in the sense of Mordukhovich. For set-valued objective mappings, we derive necessary conditions for approximately nondominated points of problems with variable domination structure taking into account the incompatibility between openness and optimality and a directional openness result for the sum of set-valued maps. We describe the necessary conditions for approximately nondominated points of set optimization problems with variable domination structure in terms of the limiting (Mordukhovich) generalized differentiation objects.

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arXiv2012

Metric regularity of composition set-valued mappings: metric setting and coderivative conditions

The paper concerns a new method to obtain a direct 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.

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arXiv2012

On Subregularity Properties of Set-Valued Mappings. Applications to Solid Vector Optimization

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.

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arXiv2011

Chain Rules for Linear Openness in Metric Spaces. Applications to Parametric Variational Systems

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 variational systems. Sharp estimates for the involved regularity moduli are given.

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arXiv2011

Openness Stability and Implicit Multifunction Theorems. Applications to Variational Systems

In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational system. Then, these results are applied in order to obtain, in a natural way, and in a widely studied case, several relations between the metric regularity moduli of the field maps defining the variational system and the solution map. Our approach allows us to complete and extend several very recent results in literature.

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arXiv2011

On Parametric Vector Optimization via Metric Regularity of Constraint Systems

Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This method allows us to present several necessary optimality conditions in solid constrained vector optimization.

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arXiv2011

Filling the Gap between Metric Regularity and Fixed Points: The Linear Openness of Compositions

This paper is devoted to the investigation of an important issue recently brought into attention by a recent paper of Arutyunov: the relation between openness of composition of set-valued maps and fixed point results. More precisely, we prove a general result concerning the openness of compositions and then we show that this result covers and implies most of the known openness results. In particular, we reobtain several recent results in this field, including a fixed point theorem of Dontchev and Frankowska.

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