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G-2026-06

IPNSDP: A solver for nonlinear semidefinite programming with automatic differentiation and chordal decomposition

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This paper introduces IPNSDP, a MATLAB solver for general Nonlinear Semidefinite Programming (NSDP) based on a second-order interior point method. Unlike linear SDP solvers, existing NSDP solvers often require users to provide difficult manual derivatives or rely on other modeling interfaces. IPNSDP addresses this by directly integrating with CasADi for automatic differentiation, significantly reducing user effort. For large-scale and structured sparse problems, it supports chordal decomposition, replacing large positive semidefinite constraints with smaller ones, enhanced by a merging strategy that combines submatrices with significant overlap to improve computational efficiency. By integrating automatic differentiation with optimized decomposition, IPNSDP offers a user-friendly scalable solution for a broad class of NSDP problems.

, 19 pages

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