SeDuMi - Optimization Package for Symmetric Cone Programming

SeDuMi (Self-Dual Minimization) is a specialized numerical computation package designed for solving symmetric cone optimization problems, particularly renowned for its applications in semidefinite programming (SDP) and second-order cone programming (SOCP). Its core strength lies in implementing high-performance interior-point method solvers that can handle complex constraints like linear matrix inequalities (LMI). The package achieves computational efficiency by transforming convex optimization problems into self-dual cone forms, leveraging the structural properties of symmetric cones.

The algorithm incorporates predictor-corrector strategies and adaptive step-size selection mechanisms, significantly reducing iteration counts while maintaining numerical stability. SeDuMi features a clean MATLAB interface design that supports seamless integration with other optimization toolboxes (such as YALMIP), facilitating modeling of complex engineering problems. From an implementation perspective, users typically define optimization variables and constraints through matrix formulations, where the solver automatically handles cone constraints through specialized barrier functions.

Typical application scenarios include control system design, combinatorial optimization, and robustness analysis, with its capability to handle large-scale sparse problems making it widely adopted in both academic research and industrial practice. Users should pay attention to duality theory in symmetric cone programming to properly establish primal-dual variable relationships. The package includes built-in functions for converting standard optimization problems into cone forms and provides detailed output including duality gaps and solution certificates.