A simple and numerical stable algorithm for solving the cone projection problem based on a Gram-Schmidt process

TL;DR

This paper introduces a straightforward, numerically stable algorithm for the cone projection problem that avoids pseudo-inverses by employing Gram-Schmidt orthonormalization, suitable for small datasets and convexity testing.

Contribution

The paper presents a novel, simple algorithm that enhances numerical stability for cone projection problems without using pseudo-inverses, improving reliability for small data sets.

Findings

Algorithm is numerically stable and simple to implement.

Suitable for small datasets and convexity tests.

Avoids pseudo-inverse computations, reducing numerical errors.

Abstract

We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse matrix is computed because of a proper Gram-Schmidt orthonormalization process that is used.