On a primal-dual Newton proximal method for convex quadratic programs

Alberto Marchi ()
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Alberto Marchi: Universität der Bundeswehr München

Computational Optimization and Applications, 2022, vol. 81, issue 2, No 2, 369-395

Abstract: Abstract This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.

Keywords: Semismooth Newton method; Proximal point method; Regularized primal-dual method; Convex quadratic programming (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-021-00342-y

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