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Jean Lasserre
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## Principal Research Fellow

LAAS-CNRS, Toulouse, France

# Inverse polynomial optimization

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### Description

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**Title**: Inverse polynomial optimization

**Author(s)**: Jean Lasserre

**Abstract**: We consider the inverse optimization problem associated with the polynomial program f^=min f(x): xin K and a given current feasible solution yin K. We provide a systematic numerical scheme to compute an inverse optimal solution. That is, we compute a polynomial tildef (which may be of same degree as f if desired) with the following properties: (a) y is a global minimizer of tildef on K with a Putinar's certificate with an a priori degree bound d fixed, and (b), tildef minimizes Vert f-tildefVert (which can be the ell1, ell2 or ellinfty-norm of the coefficients) over all polynomials with such properties. Computing tildefd reduces to solving a semidefinite program whose optimal value also provides a bound on how far is f(y) from the unknown optimal value f^. The size of the semidefinite program can be adapted to the computational capabilities available. Moreover, if one uses the ell1-norm, then tildef takes a simple and explicit canonical form. Some variations are also discussed.

**Subject**: unspecified

**Area**: Other

**Language**: English

**Year**: 2011

Affiliations : |
LAAS-CNRS, Toulouse, France |

**Journal**: Computing

**Issue**: x

**Pages**: 21

**Url**: http://arxiv.org/abs/1103.3284

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### Jean's * Peer Evaluation activity*

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- FJean Lasserre,
*Principal Research Fellow*, LAAS-CNRS, Toulouse, France.

### Jean* has...*

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- Jean Lasserre,
*Principal Research Fellow*, LAAS-CNRS, Toulouse, France.

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