Peter Richtarik – Page 2 – Optimization Online

Approximate Level Method

Published: 2009/01/08

Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization approximate projections in relative scale, large-scale optimization, level method, nonsmoth convex optimization, sensitivity analysis

In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising … Read more

Generalized power method for sparse principal component analysis

Published: 2008/11/28

Applications - Science and Engineering, Nonlinear Optimization, Nonsmooth Optimization block algorithms, gradient ascent, power method, sparse pca, strongly convex sets

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, … Read more