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This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

Optimization and Control · Mathematics 2024-01-11 Boris S. Mordukhovich , Pengcheng Wu , Xiaoqi Yang

This paper investigates full stability properties for \emph{variational Nash equilibriums} of a system of parametric nonconvex optimal control problems governed by semilinear elliptic partial differential equations. We first obtain some new…

Optimization and Control · Mathematics 2020-02-21 Nguyen Thanh Qui , Daniel Wachsmuth

In this paper, we investigate the global higher regularity properties of weak solutions for a linear elliptic system coupled with a nonlinear Maxwell-type system defined on Lipschitz domains. The regularity result is established using a…

Analysis of PDEs · Mathematics 2024-03-27 Dorothee Knees , Sebastian Owczarek , Patrizio Neff

In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a…

Analysis of PDEs · Mathematics 2019-02-13 Basang Tsering-Xiao , Wei Xiang

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…

Optimization and Control · Mathematics 2025-03-30 Mario Jelitte , Boris S. Mordukhovich

We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order PDEs. These equations arise from the inner variation of certain energy integrals. Even in the simplest model case of the Dirichlet energy the…

Analysis of PDEs · Mathematics 2019-12-19 Tadeusz Iwaniec , Leonid V. Kovalev , Jani Onninen

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…

Classical Analysis and ODEs · Mathematics 2020-02-17 H. T. Tuan , S. Siegmund

Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush--Kuhn--Tucker-type necessary optimality conditions in order to characterize local minimizers.…

Optimization and Control · Mathematics 2020-06-30 Patrick Mehlitz , Leonid I. Minchenko , Alain B. Zemkoho

In this paper, stability and sensitivity properties of a class of parametric constrained optimization problem, whose feasible region is defined by a set-valued inclusion, are investigated through the associated optimal value function.…

Optimization and Control · Mathematics 2024-12-06 Amos Uderzo

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term is allowed to be singular. Considering an operator model of the system in a Hilbert space we are interesting in the…

Dynamical Systems · Mathematics 2009-09-23 Rabah Rabah , Grigory M. Sklyar , Pavel Yu. Barkhayev

This manuscript focuses on the $\mathcal{H}_\infty$ observer design for a class of nonlinear discrete systems under the presence of measurement noise or external disturbances. Two new Linear Matrix Inequality (LMI) conditions are developed…

Systems and Control · Electrical Eng. & Systems 2024-07-12 Shivaraj Mohite

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

Analysis of PDEs · Mathematics 2015-10-19 Vo Anh Khoa

In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar…

Machine Learning · Computer Science 2017-01-20 Radu Balan , Maneesh Singh , Dongmian Zou

We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed constant rank constraint qualification.

Optimization and Control · Mathematics 2019-05-21 Ewa M. Bednarczuk , Leonid I. Minchenko , Krzysztof E. Rutkowski

This paper is devoted to the generalized differential study of the normal cone mappings associated with a large class of parametric constraint systems (PCS) that appear, in particular, in nonpolyhedral conic programming. Conducting a local…

Optimization and Control · Mathematics 2017-11-21 Helmut Gfrerer , Boris S. Mordukhovich

This paper investigates strong metric subregularity around a reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its…

Optimization and Control · Mathematics 2025-05-07 Tomáš Roubal

In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We…

Analysis of PDEs · Mathematics 2020-02-06 Bastian Harrach , Yi-Hsuan Lin

In this thesis, set-valued maps are considered to model the $i-v$ characteristics of semiconductors like diode, and transistor. Using the circuit theory laws, a generalized equation is obtained. The main concern of the thesis is to…

Optimization and Control · Mathematics 2017-04-14 Iman Mehrabinezhad

In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…

Mathematical Physics · Physics 2021-03-31 Taiki Morinaga , Shoichi Yamada