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Projection onto the exponential cone: a univariate root-finding problem

Henrik A. Friberg(haf***at***mosek.com)

Abstract: The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modeling. In this paper we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a single univariate root-finding problem. This leads to a fast algorithm shown numerically robust over a wide range of inputs.

Keywords: projection, exponential cone, relative entropy cone, julia code

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Optimization Software and Modeling Systems

Citation:

Download: [PDF]

Entry Submitted: 01/12/2021
Entry Accepted: 01/12/2021
Entry Last Modified: 01/12/2021

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