Peter Richtarik – Page 2 – Optimization Online

Simultaneously solving seven optimization problems in relative scale

Published: 2009/01/08

Linear Programming, Nonsmooth Optimization, Statistics $\ell_1hBcnorm minimization, basis pursuit, c-optimal design, centrally symmetric linear programming (cslp), elfving set, ellipsoid-squeezing method, frank-wolfe, iteratively reweighted euclidean projection (irep), iteratively reweighted least squares (irls), khachiyan's ellipsoidal rounding algorithm, linear programming, multiplicative-update method, nonsmooth convex optimization, sparse solution of underdetermined linear systems, variable-metric subgradient method

In this paper we develop and analyze an efficient algorithm which solves seven related optimization problems simultaneously, in relative scale. Each iteration of our method is very cheap, with main work spent on matrix-vector multiplication. We prove that if a certain sequence generated by the algorithm remains bounded, then the method must terminate in $O(1/\delta)$ … 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