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In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…

Optimization and Control · Mathematics 2020-06-01 Wei Peng , Hui Zhang , Xiaoya Zhang

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

Machine Learning · Computer Science 2011-12-02 Mark Schmidt , Nicolas Le Roux , Francis Bach

We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…

Logic · Mathematics 2016-10-04 Daniel Körnlein

In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…

Optimization and Control · Mathematics 2025-09-12 Kevin Huang , Nuozhou Wang , Shuzhong Zhang

The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…

Probability · Mathematics 2018-10-04 Gane Samb Lo , Modou Ngom , Tchilabola Abozou Kpanzou , Mouminou Diallo

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…

Optimization and Control · Mathematics 2021-01-21 Yekini Shehu , Olaniyi. S. Iyiola

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Optimization and Control · Mathematics 2016-05-11 Alexey Chernov , Pavel Dvurechensky , Alexander Gasnikov

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…

Optimization and Control · Mathematics 2024-06-24 R. Díaz Millán , O. P. Ferreira , J. Ugon

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…

Numerical Analysis · Mathematics 2015-09-10 Silvia Bonettini , Marco Prato

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

The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…

Numerical Analysis · Mathematics 2014-05-05 Ben Adcock , Mark Richardson

We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…

Optimization and Control · Mathematics 2024-10-04 Jean-Baptiste Fest , Tommi Heikkilä , Ignace Loris , Ségolène Martin , Luca Ratti , Simone Rebegoldi , Gesa Sarnighausen

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

Optimization and Control · Mathematics 2020-12-02 Qihang Lin , Runchao Ma , Yangyang Xu

Since introduced by Martinet and Rockafellar, the proximal point algorithm was generalized in many fruitful directions. More recently, in 2002, Pennanen studied the proximal point algorithm without monotonicity. A year later, Iusem and…

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

Numerical Analysis · Mathematics 2025-10-09 Juan Vicente Gutiérrez-Santacreu

We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…

Optimization and Control · Mathematics 2024-10-29 Ewa Bednarczuk , The Hung Tran , Monika Syga

Deep learning usually relies on training large-scale data samples to achieve better performance. However, over-fitting based on training data always remains a problem. Scholars have proposed various strategies, such as feature dropping and…

Computer Vision and Pattern Recognition · Computer Science 2022-11-22 Songhao Jiang , Yan Chu , Tianxing Ma , Tianning Zang

In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…

Information Theory · Computer Science 2016-01-06 Samet Oymak , Benjamin Recht , Mahdi Soltanolkotabi

This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function $f$. We show that for appropriate Tikhonov regularization…

Optimization and Control · Mathematics 2024-01-09 Szilárd Csaba László

This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…

Functional Analysis · Mathematics 2018-03-07 Abdul Ghaffar , Zafar Ullah , Muhammad Aqeel Ahmad Khan , Faisal Mumtaz