Computing Conjugate Barrier Information for Nonsymmetric Cones

Lea Kapelevich (), Erling D. Andersen () and Juan Pablo Vielma ()
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Lea Kapelevich: MIT
Erling D. Andersen: MOSEK ApS
Juan Pablo Vielma: Google Research and MIT Sloan School of Management

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 12, 295 pages

Abstract: Abstract The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier.

Keywords: Conjugate barrier function; Nonsymmetric cones; Interior point; 90C25; 90C51 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-022-02076-1

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