Abstract

The second-order cone is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a representation using second-order cones, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits a second-order cone representation. Based on this, we give a new algorithm to compute SONC decompositions for certain classes of nonnegative polynomials via second-order cone programming. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with a fairly large size.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.