Customized Interior-Point Methods Solver for Embedded Real-Time Convex Optimization

TL;DR

This paper introduces a specialized interior-point solver for embedded real-time convex optimization, capable of directly handling quadratic cost functions, with a code generator for efficient, sparse problem solving in guidance and control applications.

Contribution

A novel predictor-corrector primal-dual interior-point method with homogeneous embedding for quadratic SOCPs, plus a code generator for custom embedded solver implementation.

Findings

Outperforms existing solvers on embedded platform benchmarks.

Supports direct quadratic cost function handling without reformulation.

Provides a fully static, dependency-free C code generator.

Abstract

This paper presents a customized second-order cone programming (SOCP) solver tailored for embedded real-time optimization, which frequently arises in modern guidance and control (G&C) applications. The solver employs a practically efficient predictor-corrector type primal-dual interior-point method (PDIPM) combined with a homogeneous embedding framework for infeasibility detection. Unlike conventional homogeneous self-dual embedding formulations, the adopted approach can directly handle quadratic cost functions without requiring problem reformulation. This capability allows the solver to directly address quadratic objective SOCP problems, while avoiding unnecessary performance degradation caused by the loss of sparsity due to problem reformulation. To support a systematic workflow, we also develop a code generation tool that analyzes the sparsity pattern of the problem to be solved and generates customized solver code using a predefined code template. The generated solver code is written in C with no external dependencies other than the standard library math.h, and it supports complete static allocation of all data. Additionally, it provides parsing information to facilitate the use of the solver by end users. Finally, benchmark and numerical experiments on an embedded platform demonstrate that the developed solver outperforms the existing solvers on problem scales typical of G&C applications.