FDIPA-SOC: A MATLAB Package for Nonlinear Second-Order Cone Programs

This article introduces an open-source MATLAB package that implements an interior point algorithm for numerically finding the minimum of a Nonlinear Second-Order Cone Program (NSOCP). The implementation is based on the Feasible Direction Interior Point Algorithm for NSOCP (FDIPA-SOC). We have designed a user-friendly interface similar to MATLAB’s fmincon routine, and we will demonstrate how to utilize it by solving several examples of NSOCP found in the literature. Finally, we showcase an application to Machine Learning (Robust Support Vector Machine) using the software. To the best of our knowledge, this is the first open-source software made available to the scientific community for solving NSOCP.