arXiv subjects

Huu Tron Nguyen

Publications and source records attributed to Huu Tron Nguyen.

3 recordsLinked to original sources

arXiv2015

Directional Hölder Metric Regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder /Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Hölder /Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.

math.OC↗

arXiv2013

Metric Regularity of the Sum of Multifunctions and Applications

In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical multifunctions. Our results subsume some recent results by Durea and Strugariu.

math.OC↗

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.

math.FA↗