{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-active-set-method-for-sparse","title":"An active-set method for sparse approximations. Part II: General piecewise-linear terms","arxiv_id":"2302.14497","date":"2023-02-28","proceeding":null,"authors":["Spyridon Pougkakiotis","Jacek Gondzio","Dionysios S. Kalogerias"],"abstract":"In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The method exploits the structure of the piecewise-linear terms appearing in the objective in order to significantly reduce its memory requirements, and thus improve its efficiency. We showcase the robustness of the proposed solver on a variety of problems arising in risk-averse portfolio selection, quantile regression, and binary classification via linear support vector machines. We provide computational evidence to demonstrate, on real-world datasets, the ability of the solver of efficiently handling a variety of problems, by comparing it against an efficient general-purpose interior point solver as well as a state-of-the-art alternating direction method of multipliers. This work complements the accompanying paper [``An active-set method for sparse approximations. Part I: Separable $\\ell_1$ terms\", S. Pougkakiotis, J. Gondzio, D. S. Kalogerias], in which we discuss the case of separable $\\ell_1$ terms, analyze the convergence, and propose general-purpose preconditioning strategies for the solution of its associated linear systems.","url_abs":"https://arxiv.org/abs/2302.14497v1","url_pdf":"https://arxiv.org/pdf/2302.14497v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-active-set-method-for-sparse","repo_url":"https://github.com/spougkakiotis/active_set_method_for_cqp_piecewise_lp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}