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This is a continuation of our previous work entitled \enquote{Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we proposed the alternating proximal mapping method and showed convergence results on the…

Optimization and Control · Mathematics 2023-11-01 Hui Ouyang

In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…

Functional Analysis · Mathematics 2014-08-19 Kaleem Raza Kazmi

We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…

Optimization and Control · Mathematics 2014-03-25 Farzad Yousefian , Angelia Nedic , Uday V. Shanbhag

In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…

Functional Analysis · Mathematics 2009-03-10 A. Beiranvand , S. Moradi , M. Omid , H. Pazandeh

We study the convergence analysis of a Picard-S iteration method for a particular class of weak-contraction mappings. Furthermore, we prove a data dependence result for fixed point of the class of weak-contraction mappings with the help of…

Functional Analysis · Mathematics 2014-04-02 Faik Gürsoy

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators…

Optimization and Control · Mathematics 2017-08-15 Patrick L. Combettes , Lilian E. Glaudin

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

Functional Analysis · Mathematics 2013-11-05 Szilárd László

Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…

Optimization and Control · Mathematics 2024-03-27 Alexander Pichugin , Maksim Pechin , Aleksandr Beznosikov , Alexander Gasnikov

This article examines a family of smooth mappings between Banach spaces and establishes conditions for the existence of their zeros. Applications to fixed-point problems and the Implicit Function Theorem are also discussed.

Functional Analysis · Mathematics 2026-03-24 Oleg Zubelevich

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

Optimization and Control · Mathematics 2022-10-28 Patrick L. Combettes , Jean-Christophe Pesquet , Audrey Repetti

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Functional Analysis · Mathematics 2022-03-24 Neal Hermer , D. Russell Luke , Anja Sturm

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…

Optimization and Control · Mathematics 2016-08-16 I. V. Konnov

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…

Functional Analysis · Mathematics 2011-12-01 Hossein Dehghan

We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…

Statistics Theory · Mathematics 2022-11-30 Wenlong Mou , Koulik Khamaru , Martin J. Wainwright , Peter L. Bartlett , Michael I. Jordan

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

Optimization and Control · Mathematics 2025-04-16 Yunier Bello-Cruz , Max L. N. Gonçalves , Jefferson G. Melo , Cassandra Mohr

An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…

Optimization and Control · Mathematics 2020-06-29 Xueli Bai , Zheng-Hai Huang , Mengmeng Zheng

In this paper, we introduced a three-step iterative process with errors for three multivalued mappings satisfying the condition (C) in uniformly convex Banach spaces and establish strong convergence theorems for the proposed process under…

Functional Analysis · Mathematics 2011-05-12 M. Eslamian , S. Homaeipour

In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of generalized hybrid mappings in a Hilbert space. Our results…

Functional Analysis · Mathematics 2014-10-21 Sattar Alizadeh , Fridoun Moradlou

The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…

Optimization and Control · Mathematics 2024-07-29 Asrifa Sultana , Shivani Valecha