Randomized Smoothing for Stochastic Optimization

Randomized Smoothing for Stochastic Optimization

We analyze convergence rates of stochastic optimization algorithms for nonsmooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic optimization procedures, both in expectation and with high probability, that have optimal dependence on the variance of the gradient estimates. To the best of our k...

Airspace Congestion Smoothing by Stochastic Optimization

This paper addresses the general time-route assignment problem : One considers an air transportation network in a 2 dimensional space with asymmetric non-separable link cost and a eet of aircraft with their associated route and slot of departure. For each ight a set of alternative routes and a set of possible slots of departure are deened. One must nd \optimal" route and slot allocation for eac...

A Smoothing Stochastic Gradient Method for Composite Optimization

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting applications in machine learning. We propose a stochastic gradient descent algorithm for this class of optimization problem. When the non-smooth component h...

A Stochastic Optimization Model for Groundwater Management

A Stochastic Optimization Model for Groundwater Management