Related papers: Accelerated Dual-Averaging Primal-Dual Method for …
In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The…
In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…
In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…