Projecting onto a Capped Rotated Second-Order Cone

2023/07/14 by Noam Goldberg, Goldberg, Noam, Ishy Zagdoun +1
Computer Science · Engineering · Mathematics · #90 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2307.07290

openalex publication_date 2023/07/14 · openalex created_date 2023/07/18 · openalex updated_date 2026/07/28

Abstract

We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves three distinct cases, one of which reduces to the classical projection onto a second-order cone. The remaining two cases yield nontrivial projections, for which we provide necessary and sufficient conditions under which the solution lies on the intersection of the cone and a facet of a box.

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