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In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other…

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive…

We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…

We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show…

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…

Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…

In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand…

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…

We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…

Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic…

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…