Proximal-gradient algorithms for fractional programming

Algorithms for generalized fractional programming

A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ~n. The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includ...

Accelerated Proximal Gradient Methods for Nonconvex Programming

Accelerated Proximal Gradient Methods for Nonconvex Programming

Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a...

On Perturbed Proximal Gradient Algorithms

We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo batch size under which convergence is guaranteed: both increasing batch size and constant batch size are considered. We also derive non-asymptotic bounds for ...

On Stochastic Proximal Gradient Algorithms

We study a perturbed version of the proximal gradient algorithm for which the gradient is not known in closed form and should be approximated. We address the convergence and derive a non-asymptotic bound on the convergence rate for the perturbed proximal gradient, a perturbed averaged version of the proximal gradient algorithm and a perturbed version of the fast iterative shrinkagethresholding ...