Related papers: Time-Average Optimization with Non-Convex Decision…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…
We present a unified convergence analysis for first order convex optimization methods using the concept of strong Lyapunov conditions. Combining this with suitable time scaling factors, we are able to handle both convex and strong convex…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical works, a complete understanding is still missing. Apart…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…
We address the problem of distributed uncon- strained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to…
In this work we study the problem of unconstrained convex-optimization in a fully distributed multi-agent setting which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named…
Consider a set of agents collaboratively solving a distributed convex optimization problem, asynchronously, under stringent communication constraints. In such situations, when an agent is activated and is allowed to communicate with only…
This paper addresses Online Convex Optimization (OCO) problems where the constraints have additive perturbations that (i) vary over time and (ii) are not known at the time to make a decision. Perturbations may not be i.i.d. generated and…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
The distributed non-smooth resource allocation problem over multi-agent networks is studied in this paper, where each agent is subject to globally coupled network resource constraints and local feasibility constraints described in terms of…
Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness…
We study decentralized optimization where multiple agents minimize the average of their (strongly) convex, smooth losses over a communication graph. Convergence of the existing decentralized methods generally hinges on an apriori, proper…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…