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We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…

Optimization and Control · Mathematics 2026-02-06 Kevin Kurian Thomas Vaidyan , Michael P. Friedlander , Ahmet Alacaoglu

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

Optimization and Control · Mathematics 2015-09-10 Yuchen Zhang , Lin Xiao

Finite-sum optimization plays an important role in the area of machine learning, and hence has triggered a surge of interest in recent years. To address this optimization problem, various randomized incremental gradient methods have been…

Machine Learning · Computer Science 2022-06-22 Min Zhang , Yao Shu , Kun He

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…

Machine Learning · Statistics 2017-11-16 Alberto Bietti , Julien Mairal

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…

Machine Learning · Computer Science 2020-07-09 Maria-Luiza Vladarean , Ahmet Alacaoglu , Ya-Ping Hsieh , Volkan Cevher

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Optimization and Control · Mathematics 2018-11-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…

Optimization and Control · Mathematics 2018-01-03 Saeed Ghadimi

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Optimization and Control · Mathematics 2018-05-01 James V. Burke , Frank E. Curtis , Adrian S. Lewis , Michael L. Overton , Lucas E. A. Simões

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

We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the…

Optimization and Control · Mathematics 2022-06-15 Adrien Taylor , Yoel Drori

In this paper, we present the proximal-proximal-gradient method (PPG), a novel optimization method that is simple to implement and simple to parallelize. PPG generalizes the proximal-gradient method and ADMM and is applicable to…

Optimization and Control · Mathematics 2017-10-19 Ernest K. Ryu , Wotao Yin

We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…

Optimization and Control · Mathematics 2026-02-17 Neil D. Dizon , Bethany I. Caldwell , Vaithilingam Jeyakumar , Guoyin Li

In this paper we combine the stochastic variance reduced gradient (SVRG) method [17] with the primal dual fixed point method (PDFP) proposed in [7] to solve a sum of two convex functions and one of which is linearly composite. This type of…

Optimization and Control · Mathematics 2020-07-24 Ya-Nan Zhu , Xiaoqun Zhang

The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our…

Optimization and Control · Mathematics 2022-01-05 Qihang Lin , Yangyang Xu

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li

Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in…

Optimization and Control · Mathematics 2024-06-04 Zhenwei Lin , Chenyu Xue , Qi Deng , Yinyu Ye

Incremental gradient and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, without strong convexity, their convergence guarantees…

Optimization and Control · Mathematics 2024-07-01 Xufeng Cai , Jelena Diakonikolas

In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model…

Optimization and Control · Mathematics 2019-06-20 Ömer Deniz Akyildiz , Émilie Chouzenoux , Víctor Elvira , Joaquín Míguez

In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…

Optimization and Control · Mathematics 2017-03-24 Ion Necoara , Andrei Patrascu , Francois Glineur