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The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

Optimization and Control · Mathematics 2025-04-30 Boris S. Mordukhovich , Pengcheng Wu , Xiaoqi Yang

We consider a mathematical model which describes the quasistatic frictionless contact of a viscoelastic body with a rigid-plastic foundation. We describe the mechanical assumptions, list the hypotheses on the data and provide three…

Analysis of PDEs · Mathematics 2023-09-11 Piotr Bartman , Anna Ochal , Mircea Sofonea

Combining monotonicity theory related to the parametric version of the Browder-Minty Theorem with fixed point arguments we obtain hybrid existence results for a system of two operator equations. Applications are given to a system of…

Analysis of PDEs · Mathematics 2023-08-16 Michał Bełdziński , Marek Galewski , Igor Kossowski

We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar…

Functional Analysis · Mathematics 2025-02-19 Giulia Cavagnari , Giuseppe Savaré , Giacomo Enrico Sodini

In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…

Optimization and Control · Mathematics 2021-05-31 Jakub Wiktor Both

This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…

Numerical Analysis · Mathematics 2023-09-13 Pablo M. Berná , Antonio Falcó

We investigate a generalized Lagrange multiplier system in a Banach space, called a mixed variational-hemivariational inequality (MVHVI, for short), which contains a hemivariational inequality and a variational inequality. First, we employ…

Functional Analysis · Mathematics 2019-03-18 Yunru Bai , Stanislaw Migorski , Shengda Zeng

We study a new nonlinear system which contains a partial differential equation, a quasivariational inequality and a parabolic variational inequality in Banach spaces. We obtain the unique solvability of the coupled system under moderate…

Analysis of PDEs · Mathematics 2026-01-06 Wei Li , Zhenghui Tang , Zengbao Wu , Chunyan Yang

This chapter presents a self-contained approach of variational analysis and generalized differentiation to deriving necessary optimality in problems of bilevel optimization with Lipschitzian data. We mainly concentrate on optimistic models,…

Optimization and Control · Mathematics 2019-07-16 Boris S. Mordukhovich

In this paper, we study the well-posedness of a class of evolutionary variational-hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme…

Analysis of PDEs · Mathematics 2024-06-18 Nadia Skoglund Taki , Kundan Kumar

This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…

Analysis of PDEs · Mathematics 2021-12-16 Alessio Fiscella , Greta Marino , Andrea Pinamonti , Simone Verzellesi

We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of…

Optimization and Control · Mathematics 2023-06-22 Gerd Wachsmuth

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…

Analysis of PDEs · Mathematics 2012-08-14 Kamal N. Soltanov

The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…

Functional Analysis · Mathematics 2017-10-16 Jinlu Li

We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…

Optimization and Control · Mathematics 2026-05-25 Adrian Jarret , Julien Fageot

The overarching goal of this paper is to introduce and investigate a new nonlinear system driven by a nonlinear differential equation, a history-dependent quasivariational inequality, and a parabolic variational inequality in Banach spaces.…

Optimization and Control · Mathematics 2022-01-03 Xu Chu , Tao Chen , Nan-jing Huang , Yi-bin Xiao

We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $S$. We assume that $S=C\cap A^{-1}(Q)$ is the nonempty solution set of a (multiple-set) split…

Optimization and Control · Mathematics 2019-08-21 Andrzej Cegielski , Aviv Gibali , Simeon Reich , Rafał Zalas

Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…

Functional Analysis · Mathematics 2021-03-19 Vasile Berinde , Madalina Pacurar

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

Functional Analysis · Mathematics 2019-10-17 Mohammed Bachir , Gonzalo Flores , Sebastián Tapia-García

In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of…

Analysis of PDEs · Mathematics 2023-09-12 S. Migorski , YR. Bai , SD. Zeng