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We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…

Optimization and Control · Mathematics 2024-02-12 Nguyen Anh Minh , Le Dung Muu , Tran Ngoc Thang

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the…

Optimization and Control · Mathematics 2025-06-10 Meiying Wang , Hongwei Liu , Jun Yang

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

Probability · Mathematics 2024-05-14 Evan Camrud , Alain Durmus , Pierre Monmarché , Gabriel Stoltz

It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…

Machine Learning · Computer Science 2020-09-29 Vikram Krishnamurthy , George Yin

We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent…

Probability · Mathematics 2024-07-02 Keunwoo Lim , Molei Tao

Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…

Optimization and Control · Mathematics 2024-08-15 Kanji Sato , Akiko Takeda , Reiichiro Kawai , Taiji Suzuki

In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…

Optimization and Control · Mathematics 2026-03-03 Mohammad S. Alkousa , Fedor S. Stonyakin

Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…

Optimization and Control · Mathematics 2011-07-27 Yaroslav D. Sergeyev , Dmitri E. Kvasov , Falah M. H. Khalaf

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…

Machine Learning · Statistics 2025-12-02 Tim Johnston , Iosif Lytras , Nikolaos Makras , Sotirios Sabanis

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Optimization and Control · Mathematics 2024-04-16 Guy Kornowski , Ohad Shamir

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

Optimization and Control · Mathematics 2026-04-02 Albert S. Berahas , Frank E. Curtis , Lara Zebiane

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…

Statistics Theory · Mathematics 2016-12-20 Alain Durmus , Eric Moulines

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we…

Probability · Mathematics 2019-11-05 Wenlong Mou , Nicolas Flammarion , Martin J. Wainwright , Peter L. Bartlett

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…

Numerical Analysis · Mathematics 2018-06-28 Mohamed Kamel Riahi , Issam Al Qattan

In this paper, we focus on non-asymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (non-constant diffusion coefficient). More precisely, the objective of this paper is to…

Probability · Mathematics 2022-09-23 Gilles Pages , Fabien Panloup

We demonstrate that for strongly log-convex densities whose potentials are discontinuous on manifolds, the ULA algorithm converges with stepsize bias of order $1/2$ in Wasserstein-p distance. Our resulting bound is then of the same order as…

Probability · Mathematics 2023-12-05 Tim Johnston , Sotirios Sabanis

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