Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Jae-Il Jang, Chang-Hun Lee

TL;DR

The paper tackles embedded real-time convex optimization by delivering a customized predictor-corrector primal-dual interior-point solver that directly handles quadratic costs within a homogeneous embedding framework for infeasibility detection. It combines HMCP with Nesterov-Todd scaling and a Mehortra-style search direction to efficiently solve the KKT system, while leveraging offline sparsity analysis and a MATLAB-generated C implementation with static memory allocation. The authors demonstrate through benchmark suites and embedded hardware experiments that their approach outperforms existing IPM and ADMM-based solvers in both speed and reliability, particularly for small-to-medium scale SOCPs common in G&C applications. The contributions include a code-generation tool that automates solver customization for problem families, enabling memory-efficient, dependency-free embedded deployment and reducing user workload for problem updates, with practical performance gains in Mars-landing trajectory optimization and quadcopter MPC. The work significantly advances onboard optimization by delivering a scalable, robust, and hardware-friendly solver tailored to embedded G&C tasks.

Abstract

This paper presents a customized convex optimization solver tailored for embedded real-time optimization, which frequently arise 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. To support a systematic workflow, we also develop a code generation tool that analyzes the sparsity pattern of the provided problem family 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 API by end users. Benchmark results and numerical experiments on an embedded platform demonstrate that the developed solver outperforms existing solvers in both efficiency and reliability.

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

TL;DR

The paper tackles embedded real-time convex optimization by delivering a customized predictor-corrector primal-dual interior-point solver that directly handles quadratic costs within a homogeneous embedding framework for infeasibility detection. It combines HMCP with Nesterov-Todd scaling and a Mehortra-style search direction to efficiently solve the KKT system, while leveraging offline sparsity analysis and a MATLAB-generated C implementation with static memory allocation. The authors demonstrate through benchmark suites and embedded hardware experiments that their approach outperforms existing IPM and ADMM-based solvers in both speed and reliability, particularly for small-to-medium scale SOCPs common in G&C applications. The contributions include a code-generation tool that automates solver customization for problem families, enabling memory-efficient, dependency-free embedded deployment and reducing user workload for problem updates, with practical performance gains in Mars-landing trajectory optimization and quadcopter MPC. The work significantly advances onboard optimization by delivering a scalable, robust, and hardware-friendly solver tailored to embedded G&C tasks.

Abstract

This paper presents a customized convex optimization solver tailored for embedded real-time optimization, which frequently arise 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. To support a systematic workflow, we also develop a code generation tool that analyzes the sparsity pattern of the provided problem family 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 API by end users. Benchmark results and numerical experiments on an embedded platform demonstrate that the developed solver outperforms existing solvers in both efficiency and reliability.

Paper Structure

This paper contains 22 sections, 89 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Second-Order Cone Programming with a Quadratic Cost Function
  3. Solver Algorithm
  4. Interior-Point Methods
  5. Homogeneous Embedding for Quadratic Cost Functions
  6. Nesterov-Todd Scaling
  7. Search Directions
  8. Solving the Linear System
  9. Initialization
  10. Termination Criteria
  11. Overall Algorithm
  12. Solver Customization
  13. Exploiting Sparsity Patterns of the KKT System
  14. Code Generation and Parsing Information for Updating Problem Instances
  15. Benchmark Tests
  16. ...and 7 more sections

Figures (6)

  • Figure 1: Workflow of the custom solver and code generation tool developed in this study.
  • Figure 2: Performance profiles for Maros-Mészáros QP problem set
  • Figure 3: Performance profiles for portfolio optimization problem
  • Figure 4: Performance profiles for LASSO problem
  • Figure 5: Computation time results for the trajectory optimization examples
  • ...and 1 more figures