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We prove the weak and the strong convergence of the trajectories of the continuous gradient projection method under some mild assumptions on the objective function and the step size function. Moreover, we estimate the decay rate to…

Optimization and Control · Mathematics 2018-10-30 Ramzi May

We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified…

Optimization and Control · Mathematics 2022-12-13 Boris T. Polyak , Ilia A. Kuruzov , Fedor S. Stonyakin

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…

Optimization and Control · Mathematics 2023-01-03 Pham Duy Khanh , Boris S. Mordukhovich , Dat Ba Tran

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Optimization and Control · Mathematics 2016-05-30 James Renegar

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

Optimization and Control · Mathematics 2021-01-25 Yekini Shehu , Olaniyi. S. Iyiola , Xiao-Huan Li , Qiao-Li Dong

In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is…

Optimization and Control · Mathematics 2021-03-04 G. C. Bento , O. P. Ferreira , E. A. Papa Quiroz

We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our…

Optimization and Control · Mathematics 2018-12-04 Takashi Nakagaki , Mituhiro Fukuda , Sunyoung Kim , Makoto Yamashita

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…

Optimization and Control · Mathematics 2013-12-03 J. Y. Bello Cruz , G. C. Bento , G. Bouza Allende , R. F. B. Costa

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

Optimization and Control · Mathematics 2018-02-21 Zhewei Yao , Peng Xu , Farbod Roosta-Khorasani , Michael W. Mahoney

In this paper, we propose an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets. Instead of assuming the exact convex projection proposed in the literature, we allow each node to…

Systems and Control · Computer Science 2012-05-29 Youcheng Lou , Guodong Shi , Karl Henrik Johansson , Yiguang Hong

In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…

Optimization and Control · Mathematics 2021-12-14 Fedor S. Stonyakin , Seydamet S. Ablaev , Inna V. Baran

This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…

Optimization and Control · Mathematics 2024-02-12 Zhong Zheng , Shiqian Ma , Lingzhou Xue

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…

Optimization and Control · Mathematics 2010-09-21 Dan Butnariu , Yair Censor , Pini Gurfil , Ethan Hadar

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

In this paper we introduce new methods for convex optimization problems with inexact stochastic oracle. First method is an extension of the intermediate gradient method proposed by Devolder, Glineur and Nesterov for problems with inexact…

Optimization and Control · Mathematics 2015-12-08 Pavel Dvurechensky , Alexander Gasnikov

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

Optimization and Control · Mathematics 2024-11-27 O. S. Savchuk , M. S. Alkousa , A. S. Shushko , A. A. Vyguzov , F. S. Stonyakin , D. A. Pasechnyuk , A. V. Gasnikov

In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…

Optimization and Control · Mathematics 2020-04-16 Darina Dvinskikh , Alexander Tyurin , Alexander Gasnikov , Sergey Omelchenko

Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…

Optimization and Control · Mathematics 2021-08-10 Frank E. Curtis , Minhan Li