Comparison of SeDuMi and SDPT3 Solvers for Stability of Continuous-time Linear System

TL;DR

This paper empirically compares SeDuMi and SDPT3 solvers for stability analysis of continuous-time linear systems, focusing on computational efficiency, and finds SDPT3 superior in large-scale, high-precision scenarios.

Contribution

It provides a comparative analysis of SeDuMi and SDPT3 solvers' performance on stability problems using YALMIP, highlighting their efficiency differences.

Findings

SDPT3 outperforms SeDuMi in large-scale problems

SDPT3 requires less memory for high-precision calculations

Performance varies with problem size and precision

Abstract

SeDuMi and SDPT3 are two solvers for solving Semi-definite Programming (SDP) or Linear Matrix Inequality (LMI) problems. A computational performance comparison of these two are undertaken in this paper regarding the Stability of Continuous-time Linear Systems. The comparison mainly focuses on computational times and memory requirements for different scales of problems. To implement and compare the two solvers on a set of well-posed problems, we employ YALMIP, a widely used toolbox for modeling and optimization in MATLAB. The primary goal of this study is to provide an empirical assessment of the relative computational efficiency of SeDuMi and SDPT3 under varying problem conditions. Our evaluation indicates that SDPT3 performs much better in large-scale, high-precision calculations.