Conic Optimization with Spectral Functions on Euclidean Jordan Algebras

Chris Coey (), Lea Kapelevich () and Juan Pablo Vielma ()
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Chris Coey: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Lea Kapelevich: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Juan Pablo Vielma: Google Research and MIT Sloan School of Management, Cambridge, Massachusetts 02142

Mathematics of Operations Research, 2023, vol. 48, issue 4, 1906-1933

Abstract: Spectral functions on Euclidean Jordan algebras arise frequently in convex optimization models. Despite the success of primal-dual conic interior point solvers, there has been little work on enabling direct support for spectral cones , that is, 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.

Keywords: Primary: 90C51; conic optimization; interior point methods; spectral functions; Euclidean Jordan algebras; logarithmically homogeneous self-concordant barriers (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:4:p:1906-1933

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