English
Related papers

Related papers: On Lipschitzian properties of implicit multifuncti…

200 papers

The paper deals with an extension of the available theory of SCD (subspace containing derivatives) mappings to mappings between spaces of different dimensions. This extension enables us to derive workable sufficient conditions for the…

Optimization and Control · Mathematics 2022-08-03 Helmut Gfrerer , Jiri V. Outrata

In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…

Optimization and Control · Mathematics 2018-10-31 Helmut Gfrerer , Jiri V. Outrata

In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…

Optimization and Control · Mathematics 2026-04-01 Amos Uderzo

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems…

Optimization and Control · Mathematics 2019-02-21 Matúš Benko , Helmut Gfrerer , Jiří V. Outrata

In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps…

Optimization and Control · Mathematics 2023-06-22 Matúš Benko

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…

Optimization and Control · Mathematics 2023-07-31 Xiaolong Qin , Vo Duc Thinh , Jen-Chih Yao

In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…

Optimization and Control · Mathematics 2013-05-16 Amos Uderzo

In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…

Optimization and Control · Mathematics 2020-06-23 Amos Uderzo

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…

Optimization and Control · Mathematics 2017-04-04 Helmut Gfrerer , Jiří V Outrata

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…

Optimization and Control · Mathematics 2017-04-06 Amos Uderzo

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

Optimization and Control · Mathematics 2021-12-08 Helmut Gfrerer , Jiri V. Outrata

Establishing explicit formulas of coderivatives with respect to a set of the normal cone mapping to a polyhedron, the solution set of a variational inequalities system, is one of the main goals of this paper. By using our coderivative…

Optimization and Control · Mathematics 2023-12-27 Vo Duc Thinh , Xiaolong Qin , Jen-Chih Yao

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of…

Optimization and Control · Mathematics 2016-11-28 Helmut Gfrerer , Jiří V. Outrata

In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…

Optimization and Control · Mathematics 2007-05-23 M. Papi , S. Sbaraglia

In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…

General Relativity and Quantum Cosmology · Physics 2012-01-23 Henrique Gomes

We study the budget map and the indirect utility function of a parametric consumer problem in a Banach space setting by some advanced tools from set-valued and variational analysis. The Lipschitz-likeness and differentiability properties of…

Optimization and Control · Mathematics 2018-04-30 Vu Thi Huong , Jen-Chih Yao , Nguyen Dong Yen

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense…

Systems and Control · Computer Science 2021-07-07 Rushikesh Kamalapurkar , Warren E. Dixon , Andrew R. Teel

In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…

Optimization and Control · Mathematics 2015-07-01 Francisco J. Aragón Artacho , Michel H. Geoffroy

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…

Functional Analysis · Mathematics 2016-11-25 Marius Durea , Radu Strugariu

This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper…

Optimization and Control · Mathematics 2024-10-24 Wenfang Yao , Xiaoqi Yang
‹ Prev 1 2 3 10 Next ›