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

The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modelling. 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...

Full description

Saved in:
Bibliographic Details
Published inOptimization methods & software Vol. 38; no. 3; pp. 457 - 473
Main Author Friberg, Henrik A.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2023
Taylor & Francis Ltd
Subjects
90-08
Algorithms
Computational geometry
Convexity
exponential cone
Exponential functions
julia code
Projection
relative entropy cone
Robustness (mathematics)
Online AccessGet full text

Cover

More Information
Summary:The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modelling. 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 projection algorithm shown numerically robust over a wide range of inputs.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2021.2022147