Gesualdo Scutari We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned Distributed Gradient Descent (DGD) algorithm likely converges to a neighborhood of a Second-order Stationary (SoS) solution; and (ii) the more recent class … Read more
Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems. In particular, nonconvex large-scale optimization problems have found a wide range of applications in several engineering fields. The design and the analysis of such complex, large-scale, systems pose several challenges and call for the development of new optimization … Read more
We propose a novel asynchronous parallel algorithmic framework for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous … Read more
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of … Read more
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. Our framework is very flexible and includes both fully parallel Jacobi schemes and Gauss-Seidel (i.e., sequential) ones, as … Read more