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We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…

Optimization and Control · Mathematics 2019-12-17 Andrzej Ruszczynski

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…

Optimization and Control · Mathematics 2015-03-19 Dirk A. Lorenz , Marc E. Pfetsch , Andreas M. Tillmann

This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…

Optimization and Control · Mathematics 2023-01-05 Weiwei Kong , Renato D. C. Monteiro

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in…

Optimization and Control · Mathematics 2016-05-12 Mark Schmidt , Nicolas Le Roux , Francis Bach

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Optimization and Control · Mathematics 2016-05-24 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are…

Optimization and Control · Mathematics 2014-08-21 Masoud Ahookhosh , Susan Ghaderi

The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…

Optimization and Control · Mathematics 2017-05-23 Xiangru Lian , Mengdi Wang , Ji Liu

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…

Optimization and Control · Mathematics 2016-08-25 Max L. N. Goncalves , Jefferson G. Melo

In this work we propose a general nonmonotone line-search method for nonconvex multi\-objective optimization problems with convex constraints. At the $k$th iteration, the degree of nonmonotonicity is controlled by a vector $\nu_{k}$ with…

Optimization and Control · Mathematics 2024-11-15 Maria Eduarda Pinheiro , Geovani Nunes Grapiglia

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Optimization and Control · Mathematics 2025-05-20 Laurent Condat , Elnur Gasanov , Peter Richtárik

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an…

Machine Learning · Computer Science 2014-10-20 Jakub Konečný , Jie Liu , Peter Richtárik , Martin Takáč

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…

Numerical Analysis · Mathematics 2012-07-17 Erwan Faou , Fabio Nobile , Christophe Vuillot

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as…

Optimization and Control · Mathematics 2023-02-14 Hoang Tran , Qiang Du , Guannan Zhang

This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…

Optimization and Control · Mathematics 2024-01-10 I. Necoara , F. Chorobura

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…

Optimization and Control · Mathematics 2022-10-19 Martin Morin , Pontus Giselsson

We consider the problem of recovering a real-valued $n$-dimensional signal from $m$ phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objective. We establish local convergence of subgradient descent…

Machine Learning · Computer Science 2021-08-31 Paul Hand , Oscar Leong , Vladislav Voroninski

We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties…

Optimization and Control · Mathematics 2019-09-11 James V. Burke , Abraham Engle