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In this article, we aim to approximate a solution to the bilevel equilibrium problem $\mathbf{(BEP})$ for short: find $\bar{x} \in \mathbf{S}_f$ such that $ g(\bar{x}, y) \geq 0, \,\, \forall y \in \mathbf{S}_f, $ where $ \mathbf{S}_f = \{…

Optimization and Control · Mathematics 2025-03-03 Aicha Balhag , Zakaria Mazgouri , Hassan Riahi , Michel Théra

It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…

Optimization and Control · Mathematics 2018-04-30 Le Dung Muu , Phung Minh Duc , Xuan Thanh Le

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

Optimization and Control · Mathematics 2023-04-06 Caroline Geiersbach , Teresa Scarinci

We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…

Machine Learning · Computer Science 2012-06-22 Soeren Laue

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…

Numerical Analysis · Computer Science 2017-06-16 Harri Hakula , Mikael Laaksonen

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

A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…

Functional Analysis · Mathematics 2010-03-31 Dimitrios Pappas

Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…

Numerical Analysis · Mathematics 2015-06-01 Antti Hannukainen

To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically…

Optimization and Control · Mathematics 2024-04-04 Adrian S. Lewis , Genaro Lopez-Acedo , Adriana Nicolae

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

Machine Learning · Computer Science 2023-10-27 Xufeng Cai , Ahmet Alacaoglu , Jelena Diakonikolas

We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…

Optimization and Control · Mathematics 2024-07-12 Nam V Tran , Hai T. T. Le , An V. Truong , Vuong T. Phan

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

Machine Learning · Statistics 2022-07-18 Junhong Lin , Alessandro Rudi , Lorenzo Rosasco , Volkan Cevher

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…

Optimization and Control · Mathematics 2024-10-30 Emile Simon , Vincent Wertz

This paper deals with an implicit Newton-like inertial dynamical system governed by a maximally comonotone inclusion problem in a Hilbert space. Under suitable conditions, we establish not only pointwise estimates and integral estimates for…

Optimization and Control · Mathematics 2024-05-13 Z. Z. Tan , R. Hu , Y. P. Fang

We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this…

Algebraic Geometry · Mathematics 2020-07-06 Anton Leykin , Abraham Martin del Campo , Frank Sottile , Ravi Vakil , Jan Verschelde

Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this…

Optimization and Control · Mathematics 2025-03-18 Shima Shabani , Michael Breuß

This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…

Optimization and Control · Mathematics 2026-05-27 Xin Qu , Wei Bian , Xiaojun Chen

In this paper, we propose an inexact golden ratio primal-dual algorithm with linesearch step(IP-GRPDAL) for solving the saddle point problems, where two subproblems can be approximately solved by applying the notations of inexact extended…

Optimization and Control · Mathematics 2025-09-23 Changjie Fang , Jinxiu Liu , Jingtao Qiu , Shenglan Chen

In this paper, we propose new extragradient algorithms for solving a split equilibrium and nonexpansive mapping SEPNM($C, Q, A, f, g, S, T)$ where $C, Q$ are nonempty closed convex subsets in real Hilbert spaces $\mathcal{H}_1,…

Optimization and Control · Mathematics 2015-09-17 Bui Van Dinh , Dang Xuan Son , Tran Viet Anh

In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…

Numerical Analysis · Mathematics 2017-01-12 Liu Yang , Yuquan Sun , Fanghui Gong