2021/03/06 by Chris Coey, Coey, Chris, Lea Kapelevich +3 · 2 citations
Computer Science · Mathematics · #90C51 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2103.04104
openalex publication_date 2021/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spectral functions on Euclidean Jordan algebras arise frequently in convex models. Despite the success of primal-dual conic interior point solvers, there has been little work on enabling direct support for spectral cones, i.e. proper nonsymmetric cones defined from epigraphs and perspectives of spectral functions. We propose simple logarithmically homogeneous barriers for spectral cones and we derive efficient, numerically stable procedures for evaluating barrier oracles such as inverse Hessian operators. For two useful classes of spectral cones - the root-determinant cones and the matrix monotone derivative cones - we show that the barriers are self-concordant, with nearly optimal parameters. We implement these cones and oracles in our open source solver Hypatia, and we write simple, natural formulations for four applied problems. Our computational benchmarks demonstrate that Hypatia often solves the natural formulations more efficiently than advanced solvers such as MOSEK 9 solve equivalent extended formulations written using only the cones these solvers support.