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3410. Lifting nonnegativity over general semialgebraic sets to nonnegativity over simple sets.
Invited abstract in session MD-38: Applications of conic optimization, stream Conic Optimization: Theory, Algorithms, and Applications.
Monday, 14:30-16:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Juan Vera
|
| Etrie and OR, Tilburg University |
Abstract
Semidefinite optimization hierarchies are the standard approach to Polynomial Optimization and generalized moment problems. Several authors have proposed hierarchies based on other conic alternatives lately. These alternatives replace the sum of squares with different classes of non-negative polynomials. The convergence of such hierarchies is rooted in Positivtellensatze, which guarantee particular types of non-negative certificates.
We propose a universal approach to derive new Positivstellensatze for general semialgebraic sets from ones developed for simpler sets, such as a box or a simplex. We illustrate the approach by constructing Positivstellensatze over compact semialgebraic sets based on any given cone of non-negative polynomials. Also, we show how to use our results to derive sparse Psatz and to extend them to unbounded semialgebraic sets.
Keywords
- Programming, Semidefinite
- Programming, Nonlinear
- Continuous Optimization
Status: accepted
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