Related papers: Comparison of Proximal First-Order Primal and Prim…
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Combinatorica 15(3):435-454, 1995).…
The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
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…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…
We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a…
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by solving convex programs. Finding the worst-case performance of…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
We present a methodology to automatically compute worst-case performance bounds for a large class of first-order decentralized optimization algorithms. These algorithms aim at minimizing the average of local functions that are distributed…