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In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…

Optimization and Control · Mathematics 2018-11-09 Veronika Karl , Frank Pörner

In this paper by using $W_{n}$-mapping, we introduce a composite iterative method for finding a common fixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality. Furthermore, the strong…

Functional Analysis · Mathematics 2013-08-19 Vahid Darvish , S. M. Vaezpour

Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by…

Computer Science and Game Theory · Computer Science 2025-11-06 Aloïs Duguet , Tobias Harks , Martin Schmidt , Julian Schwarz

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

Functional Analysis · Mathematics 2020-06-26 Rui Wang , Yuesheng Xu

In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by…

Functional Analysis · Mathematics 2019-11-19 Tatsuki Ezawa , Yasunori Kimura

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

Optimization and Control · Mathematics 2024-12-11 Gabriela Kováčová , Birgit Rudloff

In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called…

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences…

Optimization and Control · Mathematics 2009-09-21 Jean-Philippe Chancelier

In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…

Optimization and Control · Mathematics 2019-02-26 Fabio Botelho

We consider a class of elliptic quasivariational inequalities in a reflexive Banach space $X$ for which we recall a convergence criterion obtained in [10]. Each inequality $\cal P$ in the class is governed by a set of constraints $K$ and…

Analysis of PDEs · Mathematics 2024-09-25 Piotr Bartman-Szwarc , Anna Ochal , Mircea Sofonea , Domingo A. Tarzia

We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is…

Optimization and Control · Mathematics 2021-05-07 Mattia Bianchi , Giuseppe Belgioioso , Sergio Grammatico

This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…

Optimization and Control · Mathematics 2025-09-09 Watanjeet Singh , Sumit Chandok

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Computational Engineering, Finance, and Science · Computer Science 2023-05-23 Juan F. Giraldo , Victor M. Calo

In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…

Optimization and Control · Mathematics 2018-05-08 Bui Van Dinh , Nguyen Ngoc Hai , Do Sang Kim

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

Quantum Physics · Physics 2009-09-07 David Taj

In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…

General Mathematics · Mathematics 2022-05-10 Nikos Mantzakouras , Eteri Biragova

It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty…

Functional Analysis · Mathematics 2015-11-24 Sławomir Borzdyński , Andrzej Wiśnicki

We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to…

Numerical Analysis · Mathematics 2024-11-20 Øyvind Stormark Auestad

The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence…

Optimization and Control · Mathematics 2013-05-21 Heinz H. Bauschke , Hung M. Phan , Xianfu Wang

We review the theory of Va\u{i}nberg--Br\`{e}gman relative entropies and quasinonexpansive operators on reflexive Banach spaces, and obtain several new results. We also develop an extension of this theory to nonreflexive Banach spaces,…

Functional Analysis · Mathematics 2026-02-17 Ryshard-Pavel Kostecki