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In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…

Optimization and Control · Mathematics 2015-10-28 Dang Van Hieu

This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…

Systems and Control · Electrical Eng. & Systems 2024-03-05 Juho Bae , Ji Hoon Bai , Byung-Yoon Lee , Jun-Yong Lee

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…

Optimization and Control · Mathematics 2009-12-23 Y. Censor , W. Chen , P. L. Combettes , R. Davidi , G. T. Herman

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…

Computer Vision and Pattern Recognition · Computer Science 2026-04-24 Frederik L. Dennig , Daniel A. Keim

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

Optimization and Control · Mathematics 2023-07-18 Jan Harold Alcantara , Ching-pei Lee

A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once…

Numerical Analysis · Mathematics 2025-10-02 Xiaoming Zheng , Kun Zhao , Jiahong Wu , Weiwei Hu , Dapeng Du

Constrained convex optimization problems arise naturally in many real-world applications. One strategy to solve them in an approximate way is to translate them into a sequence of convex feasibility problems via the recently developed level…

Optimization and Control · Mathematics 2019-04-30 E. Bonacker , A. Gibali , K. -H. Küfer

We study the generic behavior of Hamiltonian trajectories on a regular level set in the cotangent bundle, after projection to the base. We prove that for a generic submersive level set, projected trajectories have discrete…

Dynamical Systems · Mathematics 2026-02-18 Lucas Dahinden , Jacobus de Pooter

In this work, we propose an efficient two-metric adaptive projection method for solving the $\ell_1$-norm minimization problem. Our approach is inspired by the two-metric projection method, a simple yet elegant algorithm proposed by…

Optimization and Control · Mathematics 2026-04-16 Hanju Wu , Yue Xie

In this paper we find the optimal error bound (smallest possible estimate, independent of the starting point) for the linear convergence rate of the simultaneous projection method applied to closed linear subspaces in a real Hilbert space.…

Optimization and Control · Mathematics 2017-09-15 Simeon Reich , Rafał Zalas

Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…

Optimization and Control · Mathematics 2025-06-30 Didier Aussel , Jauny , Asrifa Sultana , Shivani Valecha

We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…

Functional Analysis · Mathematics 2012-11-08 Heinz H. Bauschke , Jiawei Chen , Xianfu Wang

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently…

Graphics · Computer Science 2020-11-05 Martin Skrodzki , Eric Zimmermann , Konrad Polthier

In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly…

Optimization and Control · Mathematics 2017-02-06 Aviv Gibali , Simeon Reich , Rafal Zalas

We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces. For Banach spaces which are convex and smooth of power type,…

Functional Analysis · Mathematics 2020-10-09 Christian Bargetz , Emir Medjic

The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared…

Optimization and Control · Mathematics 2018-05-08 Roberto Cominetti , Vera Roshchina , Andrew Williamson

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…

Optimization and Control · Mathematics 2023-06-08 Chenzheng Guo , Jing Zhao

In 1997, Bauschke, Borwein, and Lewis have stated a trichotomy theorem that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem.…

Functional Analysis · Mathematics 2007-10-15 H. H. Bauschke , F. Deutsch , H. Hundal

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

Optimization and Control · Mathematics 2010-09-28 Y. Censor , R. Davidi , G. T. Herman

We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…

Statistics Theory · Mathematics 2018-09-07 Victor-Emmanuel Brunel