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A relaxed-certificate facial reduction algorithm based on subspace intersection

Henrik A. Friberg (metronware***at***gmail.com)

Abstract: A ``facial reduction''-like regularization algorithm is established for conic optimization problems by relaxing requirements on the reduction certificates. It requires only a linear number of reduction certificates from a constant time-solvable auxiliary problem, but is challenged by representational issues of the exposed reductions. A condition for representability is presented, analyzed for Cartesian product cones, and shown satisfiable for all exposed reductions of a single second-order cone. Should the representational condition fail at any iteration, a partially regularized problem is still obtained. Work on representing the exposed reductions, i.e., subspace intersections of conic sets, is ongoing.

Keywords: Facial reduction, subspace intersection, conic optimization, second-order cones

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )


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Entry Submitted: 01/13/2016
Entry Accepted: 01/13/2016
Entry Last Modified: 07/12/2016

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