Projecting onto a Capped Rotated Second-Order Cone
Optimization and Control
2025-07-16 v3
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.
Cite
@article{arxiv.2307.07290,
title = {Projecting onto a Capped Rotated Second-Order Cone},
author = {Noam Goldberg and Ishy Zagdoun},
journal= {arXiv preprint arXiv:2307.07290},
year = {2025}
}