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On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming

Abstract : This report is devoted to the study of robust semidefinite programming. We show that to the issue of computing the worst-case optimal value of semidefinite programs depending polynomially upon a finite number of bounded scalar parameters, one may associate a countable family of standard semidefinite programs, whose optimal values converge monotonically towards the requested quantity. The results is linked to representation formula and positiveness criterion for matrix-valued polynomials.
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https://hal.inria.fr/inria-00071674
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Submitted on : Tuesday, May 23, 2006 - 6:29:57 PM
Last modification on : Friday, February 4, 2022 - 3:13:13 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:32:41 PM

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  • HAL Id : inria-00071674, version 1

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Pierre-Alexandre Bliman. On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming. [Research Report] RR-4906, INRIA. 2003. ⟨inria-00071674⟩

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