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The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the…

Optimization and Control · Mathematics 2020-02-28 Stefano Lucidi , Mauro Passacantando , Francesco Rinaldi

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…

Functional Analysis · Mathematics 2026-03-19 Watanjeet Singh , Sumit Chandok

The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…

Optimization and Control · Mathematics 2015-10-30 Dang Van Hieu

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of…

Optimization and Control · Mathematics 2014-07-09 G. C. Bento , J. X. Cruz Neto , J. O. Lopes , P. A. Soares , A. Soubeyran

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order…

Quantum Physics · Physics 2024-10-22 Chengchang Liu , Chaowen Guan , Jianhao He , John C. S. Lui

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Optimization and Control · Mathematics 2025-12-12 Chenglong Bao , Yancheng Yuan , Shulan Zhu

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…

Optimization and Control · Mathematics 2025-08-20 Chee-Khian Sim

This paper studies the behavior of the extragradient algorithm [Korpelevich, 1976] when applied to hypomonotone operators, a class of problems that extends beyond the classical monotone setting. To support the understanding of this…

Optimization and Control · Mathematics 2025-01-20 Khaled Alomar , Tatjana Chavdarova

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…

Optimization and Control · Mathematics 2023-11-22 Alexander Titov , Fedor Stonyakin , Mohammad Alkousa , Alexander Gasnikov

In this article, we provide a modification to the Bregman Golden Ratio Algorithm (B-GRAAL). We analyze the B-GRAAL algorithm with a new step size rule, where the step size increases after a certain number of iterations and does not require…

Optimization and Control · Mathematics 2025-03-11 Gourav Kumar , V. Vetrivel

We study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with…

Functional Analysis · Mathematics 2016-11-08 Hadi Khatibzadeh , Vahid Mohebbi

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in…

Optimization and Control · Mathematics 2021-07-27 Bing Tan , Jingjing Fan , Songxiao Li

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Optimization and Control · Mathematics 2025-01-28 Huaqing Zhang , Lesi Chen , Jing Xu , Jingzhao Zhang

For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…

Optimization and Control · Mathematics 2025-03-18 Huang Chengzhi

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Optimization and Control · Mathematics 2023-10-04 Xiaoxue Jiang

In this paper, a new mixed finite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains. The proposed scheme doesn't involve any integration along…

Numerical Analysis · Mathematics 2020-05-26 Huangxin Chen , Amiya K. Pani , Weifeng Qiu