Papers › An active-set method for sparse approximations. Part II: General piecewise-linear terms
An active-set method for sparse approximations. Part II: General piecewise-linear terms
Spyridon Pougkakiotis, Jacek Gondzio, Dionysios S. Kalogerias
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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 ℓ₁ terms", S. Pougkakiotis, J. Gondzio, D. S. Kalogerias], in which we discuss the case of separable ℓ₁ terms, analyze the convergence, and propose general-purpose preconditioning strategies for the solution of its associated linear systems.
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