Name
Title | ||
|---|---|---|
Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations |
Abstract | ||
|---|---|---|
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are large and costly to solve when the polynomials involved in the SOS programs have a large number of variables and degree. In this paper, we review SOS optimization techniques and present two new methods for improving their computational efficiency. The first method leverages the sparsity of the underlying SDP to obtain computational speed-ups. Further improvements can be obtained if the coefficients of the polynomials that describe the problem have a particular sparsity pattern, called chordal sparsity. The second method bypasses semidefinite programming altogether and relies instead on solving a sequence of more tractable convex programs, namely linear and second order cone programs. This opens up the question as to how well one can approximate the cone of SOS polynomials by second order representable cones. In the last part of the paper, we present some recent negative results related to this question. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1109/CDC.2017.8263706 | 2017 IEEE 56th Annual Conference on Decision and Control (CDC) |
Keywords | Field | DocType |
semidefinite program,SOS programs,SOS optimization techniques,computational efficiency,underlying SDP,particular sparsity pattern,semidefinite programming,tractable convex programs,linear order cone programs,second order cone programs,SOS polynomials,chordal sparsity,sum of squares optimization | Bottleneck,Mathematical optimization,Polynomial,Chordal graph,Regular polygon,Sum-of-squares optimization,Explained sum of squares,Mathematics,Semidefinite programming,Scalability | Conference |
ISSN | ISBN | Citations |
0743-1546 | 978-1-5090-2874-0 | 3 |
PageRank | References | Authors |
0.42 | 23 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Amir Ali Ahmadi | 1 | 267 | 21.34 |
| georgina hall | 2 | 14 | 2.43 |
| Antonis Papachristodoulou | 3 | 990 | 90.01 |
| James Saunderson | 4 | 97 | 8.80 |
| Yang Zheng | 5 | 267 | 18.67 |