Related papers: Accelerated First-Order Methods for Hyperbolic Pro…
We present a simple transformation of any linear program or semidefinite program into an equivalent convex optimization problem whose only constraints are linear equations. The objective function is defined on the whole space, making…
Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient…
This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…
This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
A set of accelerated first order algorithms with memory are proposed for minimising strongly convex functions. The algorithms are differentiated by their use of the iterate history for the gradient step. The increased convergence rate of…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…