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In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

Optimization and Control · Mathematics 2020-06-17 Ernö Robert Csetnek , Yura Malitsky , Matthew K. Tam

We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…

Optimization and Control · Mathematics 2019-12-20 Sebastian Banert , Radu Ioan Bot , Ernö Robert Csetnek

Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators…

Optimization and Control · Mathematics 2021-04-13 Minh N. Dao , Hung M. Phan

We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…

Functional Analysis · Mathematics 2014-07-02 Radu Ioan Bot , Ernö Robert Csetnek

By suitable examples we illustrate an algorithm for composition of inverse problems.

History and Overview · Mathematics 2014-11-24 Julia Ninova , Vesselka Mihova

In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…

Numerical Analysis · Mathematics 2023-06-09 Cong Guo , Chenliang Li , Tao Luo

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

Optimization and Control · Mathematics 2017-11-07 Renato D. C. Monteiro , Chee-Khian Sim

Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and…

Optimization and Control · Mathematics 2019-10-25 Han Wang , Mahyar Fazlyab , Shaoru Chen , Victor M. Preciado

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…

Numerical Analysis · Mathematics 2025-08-07 Chinmay Kumar Giri , Debasisha Mishra

In this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of split variational inequality problem, quasi-variational and variational inequality problems in Hilbert spaces. Using projection…

Optimization and Control · Mathematics 2013-08-14 Kaleem Raza Kazmi

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…

Numerical Analysis · Mathematics 2008-04-22 N. S. Hoang , A. G. Ramm

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Optimization and Control · Mathematics 2017-06-20 Quang Van Nguyen , Olivier Fercoq , Volkan Cevher

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Optimization and Control · Mathematics 2023-12-05 Yurii Nesterov

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

In this paper, we propose and study several strongly convergent versions of the forward-reflected-backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed…

Optimization and Control · Mathematics 2022-08-16 Chinedu Izuchukwu , Simeon Reich , Yekini Shehu , Adeolu Taiwo

In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed…

Optimization and Control · Mathematics 2021-09-22 Luis M. Briceño-Arias , Fernando Roldán

Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a…

Optimization and Control · Mathematics 2012-09-18 Suvrit Sra

We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…

Optimization and Control · Mathematics 2025-02-13 Dmitrii Lozovanu

We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…

Combinatorics · Mathematics 2023-06-22 János Balogh , Cosmin Bonchiş , Diana Diniş , Gabriel Istrate , Ioan Todinca