A Semismooth Newton Method with Multidimensional Filter Globalization for $l_1$-Optimization

Autor:	Michael Ulbrich, Andre Milzarek
Rok vydání:	2014
Předmět:	Mathematical optimization Optimization problem Regular polygon Thresholding Theoretical Computer Science Range (mathematics) symbols.namesake Filter (video) Fixed-point iteration Convergence (routing) symbols Newton's method Software Mathematics
Zdroj:	SIAM Journal on Optimization. 24:298-333
ISSN:	1095-7189 1052-6234
Popis:	Due to their property of enhancing the sparsity of solutions, $l_1$-regularized optimization problems have developed into a highly dynamic research area with a wide range of applications. We present a class of methods for $l_1$-regularized optimization problems that are based on a combination of semismooth Newton steps, a filter globalization, and shrinkage/thresholding steps. A multidimensional filter framework is used to control the acceptance and to evaluate the quality of the semismooth Newton steps. If the current Newton iterate is rejected a shrinkage/thresholding-based step with quasi-Armijo stepsize rule is used instead. Global convergence and transition to local q-superlinear convergence for both convex and nonconvex objective functions are established. We present numerical results and comparisons with several state-of-the-art methods that show the efficiency and competitiveness of the proposed method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b7963a0cccc9a7bba18646d4212aa79e https://doi.org/10.1137/120892167 Zobrazit plný text záznamu