Convexity in semi-algebraic geometry and polynomial optimization
| dc.creator | Lasserre, Jean B. | |
| dc.date | 2008-06-23 | |
| dc.date | 2008-12-04 | |
| dc.date.accessioned | 2026-07-07T12:08:58Z | |
| dc.date.available | 2026-07-07T12:08:58Z | |
| dc.description | We review several (and provide new) results on the theory of moments, sums of squares and basic semi-algebraic sets when convexity is present. In particular, we show that under convexity, the hierarchy of semidefinite relaxations for polynomial optimization simplifies and has finite convergence, a highly desirable feature as convex problems are in principle easier to solve. In addition, if a basic semi-algebraic set K is convex but its defining polynomials are not, we provide a certificate of convexity if a sufficient (and almost necessary) condition is satified. This condition can be checked numerically and also provides a new condition for K to have semidefinite representation. For this we use (and extend) some of recent results from the author and Helton and Nie. Finally, we show that when restricting to a certain class of convex polynomials, the celebrated Jensen's inequality in convex analysis can be extended to linear functionals that are not necessarily probability measures. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0806.3784 | |
| dc.identifier | http://arxiv.org/abs/0806.3784 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209477 | |
| dc.subject | Optimization and Control | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14P10; 90C22; 11E25; 12D15; 90C25 | |
| dc.title | Convexity in semi-algebraic geometry and polynomial optimization | |
| dc.type | text |