Implementation of a projection and rescaling algorithm for second-order conic feasibility problems

This paper documents a computational implementation of a projection and rescaling algorithm for solving one of the alternative feasibility problems find x is an element of L boolean AND Omega or find (x) over cap is an element of L-perpendicular to boolean AND Omega, where L is a linear subspace in R-n, L-perpendicular to is its orthogonal complement, and Omega subset of R-n is the interior of a direct product of second order cones. The gist of the projection and rescaling algorithm is to enhance a low-cost first-order method (a basic procedure) with an adaptive reconditioning transformation (a rescaling step). We give a full description of a Python implementation of this algorithm and present multiple sets of numerical experiments on synthetic problem instances with varied levels of conditioning. Our computational experiments provide promising evidence of the effectiveness of the projection and rescaling algorithm. Our Python code is publicly available. Furthermore, the simplicity of the algorithm makes a computational implementation in other environments completely straightforward.