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We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet

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

Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for…

Optimization and Control · Mathematics 2019-06-28 Maxim Balashov , Boris Polyak , Andrey Tremba

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…

Optimization and Control · Mathematics 2019-10-14 Tao Sun , Yuejiao Sun , Dongsheng Li , Qing Liao

We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…

Optimization and Control · Mathematics 2024-04-18 Yunier Bello-Cruz , J. G. Melo , L. F. Prudente , R. V. G. Serra

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

Optimization and Control · Mathematics 2019-11-12 Aviv Gibali , Karl-Heinz Küfer , Daniel Reem , Philipp Süss

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

Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…

Optimization and Control · Mathematics 2021-03-22 Harshal D. Kaushik , Farzad Yousefian

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…

Optimization and Control · Mathematics 2013-03-12 Nicolas Le Roux , Mark Schmidt , Francis Bach

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

Optimization and Control · Mathematics 2026-04-01 John Chiang

This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…

Optimization and Control · Mathematics 2024-08-13 Pritpal Matharu , Bartosz Protas

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Machine Learning · Computer Science 2024-12-17 Naoki Sato , Koshiro Izumi , Hideaki Iiduka

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

Numerical Analysis · Mathematics 2013-01-01 I. Daubechies , M. Fornasier , I. Loris

Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…

Machine Learning · Computer Science 2013-04-03 Lijun Zhang , Tianbao Yang , Rong Jin , Xiaofei He

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…

Optimization and Control · Mathematics 2019-10-14 Jelena Diakonikolas , Alejandro Carderera , Sebastian Pokutta

In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the…

Optimization and Control · Mathematics 2014-09-23 Yiming Yan

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

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

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

Optimization and Control · Mathematics 2019-11-19 Fan Zhang , Hao Wang , Jiashan Wang , Kai Yang