Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part I: Model and Convergence

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

Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part II: Complexity and Numerical Results

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

Parallel Algorithms for Big Data Optimization

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

A game-theoretic approach to computation offloading in mobile cloud computing

We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier of mobile nodes, a middle tier (cloudlets) of nearby computing nodes, typically located at the mobile nodes access points but characterized by a limited amount of resources, and a remote tier of distant cloud servers, which have practically infinite … Read more

A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that … Read more

A Family of Newton Methods for Nonsmooth Constrained Systems with Nonisolated Solutions

We propose a new family of Newton-type methods for the solution of constrained systems of equations. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, local, quadratic convergence to a solution of the system of equations can be established. We show that as particular instances of the method we obtain inexact … Read more

An LP-Newton Method: Nonsmooth Equations, KKT Systems, and Nonisolated Solutions

We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. … Read more