We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global O(1/ √ T ) convergence rate for any convex function which is locally Lipschitz around its minimizers. This approach is based on Shor’s classic subgradient analysis and implies generalizations of the standard convergenc...

The Nonnegative Matrix Factorization (NMF) has become an increasingly popular approach in many areas of telecommunications. A number of properties and a nonlinear programming formulation for NMF are introduced, which allow approximations to the solution of diverse image processing problems, ranging from data analysis to video summarization, pattern recognition and image reconstruction. A spectr...

One class classification is widely used in many applications. Only one target class is well characterized by instances in the training data in one class classification, and no instance is available for other non-target classes, or few instances are present and they cannot form statistically representative samples for the negative concept. A two-step paradigm employing nonnegative matrix factori...

Regularization of ill-posed linear inverse problems via l1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an l1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to l1-constraints, using a gradient method, with projection on l1-balls. The correspondin...

We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript “A distributed primal-dual algorithm for computation of ge...

We introduce a method for deriving aerosol spectral radiative forcing along with single scattering albedo, asymmetry parameter, and surface albedo from airborne vertical profile measurements of shortwave spectral irradiance and spectral aerosol optical thickness. The new method complements the traditional, direct measurement of aerosol radiative forcing efficiency from horizontal flight legs be...

An eecient method (DACG, Deeated Accelerated Conjugate Gradient) has recently been developed, based on the conjugate gradient (CG) minimization of the Rayleigh quotient over successive deeated subspaces of decreasing size. A new version of this algorithm is presented and discussed to evaluate the 40 leftmost eigenpairs of FE problems of increasing size up to 10500. Its asymptotic convergence ra...