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Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive errors. Within a nonconvex semialgebraic framework, assuming…

Optimization and Control · Mathematics 2025-05-14 Jérôme Bolte , Tam Le , Éric Moulines , Edouard Pauwels

We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…

Optimization and Control · Mathematics 2021-12-20 Lorenzo Lampariello , Gianluca Priori , Simone Sagratella

We investigate an inertial viscosity-type Tseng's extragradient algorithm with a new step size to solve pseudomonotone variational inequality problems in real Hilbert spaces. A strong convergence theorem of the algorithm is obtained without…

Optimization and Control · Mathematics 2020-07-24 Bing Tan , Xiaolong Qin

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…

Optimization and Control · Mathematics 2020-11-23 Tristan van Leeuwen , Aleksandr Aravkin

Bilevel programs model sequential decision interactions between two sets of players and find wide applications in real-world complex systems. In this paper, we consider a bilevel mixed-integer linear program with binary tender, wherein the…

Optimization and Control · Mathematics 2025-09-03 Bo Zhou , Ruiwei Jiang , Siqian Shen

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

Numerical Analysis · Mathematics 2020-11-16 F. Frühauf , O. Scherzer , A. Leitao

We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…

Optimization and Control · Mathematics 2026-01-16 Frank E. Curtis , Xiaoyi Qu , Daniel P. Robinson

Single-call stochastic extragradient methods, like stochastic past extragradient (SPEG) and stochastic optimistic gradient (SOG), have gained a lot of interest in recent years and are one of the most efficient algorithms for solving…

Optimization and Control · Mathematics 2023-11-14 Sayantan Choudhury , Eduard Gorbunov , Nicolas Loizou

In this paper, we study a class of generalized inverse mixed variational inequality problems (GIMVIPs). We propose a novel projection-based second-order time-varying dynamical system for solving GIMVIPs. Under the assumptions that the…

Optimization and Control · Mathematics 2026-01-23 Nam Van Tran

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

Numerical Analysis · Mathematics 2018-06-05 Robert Plato , Bernd Hofmann

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits…

Optimization and Control · Mathematics 2023-01-25 M. Marques Alves , Marina Geremia , Raul T. Marcavillaca

In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive…

Functional Analysis · Mathematics 2014-09-17 Ibrahim Karahan

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…

Optimization and Control · Mathematics 2020-06-03 Le Thi Khanh Hien , Nicolas Gillis , Panagiotis Patrinos

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Methodology · Statistics 2020-08-17 Ana F. Vidal , Valentin De Bortoli , Marcelo Pereyra , Alain Durmus

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

Analysis of PDEs · Mathematics 2019-11-06 Guangyu Gao , Bo Han , Shanshan Tong

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

Optimization and Control · Mathematics 2024-06-03 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…

Numerical Analysis · Mathematics 2022-05-12 Gaurav Mittal , Ankik Kumar Giri

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

The present study is an extension of the work done in Parareal convergence for oscillatory pdes with finite time-scale separation (2019), A. G. Peddle, T. Haut, and B. Wingate, [16], and An asymptotic parallel-in-time method for highly…

Numerical Analysis · Mathematics 2023-03-17 Juliane Rosemeier , Terry Haut , Beth Wingate

This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component…

Machine Learning · Computer Science 2019-07-03 Feiping Nie , Zhanxuan Hu , Xiaoqian Wang , Rong Wang , Xuelong Li , Heng Huang