Related papers: A FISTA-Type First Order Algorithm on Composite Op…
This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…
Stochastic optimization methods have actively been playing a critical role in modern machine learning algorithms to deliver decent performance. While numerous works have proposed and developed diverse approaches, first-order and…
Second-order methods for convex optimization outperform first-order methods in terms of theoretical iteration convergence, achieving rates up to $O(k^{-5})$ for highly-smooth functions. However, their practical performance and applications…
Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
The "Inertial Forward-Backward algorithm" (IFB) is a powerful tool for convex nonsmooth minimization problems, it gives the well known "fast iterative shrinkage-thresholding algorithm " (FISTA), which enjoys $O\left( {\frac{1}{{{k^2}}}}…
Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and…
Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In…
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by…
In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
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…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function \omega with a linear transformation. This setting includes Group Lasso methods,…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical…