The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M≤k of real m× n matrices of rank at most k. Such methods extend Riemannian optimization methods, which are successfully used on the smooth manifold Mk of rank-k matrices, to its closure by taking steps along gradient-related directions in the tangent cone, and afterwards proje...

In this paper, we propose a new nonlinear conjugate gradient method for large-scale unconstrain optimization which possesses the following properties:(i)the sufficient descent condition −g k dk ≥ 7 8 ‖gk‖ 2 holds without any line searches;(ii)With exact line search, this method reduces to a nonlinear version of the Liu-Storey conjugate gradient scheme.(iii)Under some assumption, global converge...

Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior ...

A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel manifold, which are known to converge globally under mild conditions. To determine the convergence rate of these methods, we give an explicit estimate of the ...

In this paper we describe methods for improving the RWTH German speech recognizer used within the VERBMOBIL project. In particular, we present acceleration methods for the search based on both within-word and across-word phoneme models. The recognizer in the VERBMOBIL project is used in an online environment. We will discuss some incremental methods to reduce the response time of an on-line spe...