- Inverse polynomial optimization Jean B Lasserre(lasserrelaas.fr) Abstract: We consider the inverse optimization problem associated with the polynomial program $f^*=\min \{f(x):x\inK\}$ and a given current feasible solution $y\in K$. We provide a numerical scheme to compute an inverse optimal solution. That is, we compute a polynomial $\tilde{f}$ (which may be of same degree as $f$ if desired) with the following properties: (a) $y$ is a global minimizer of $\tilde{f}$ on $K$ with a Putinar's certificate with an a priori degree bound fixed, and (b), $\tilde{f}$ minimizes $\Vert f-\tilde{f}\Vert$ (which can be the $\ell_1$, $\ell_2$ or $\ell_\infty$-norm of the coefficients) over all polynomials with such properties. Computing $\tilde{f}_d$ 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 $\ell_1$-norm, then $\tilde{f}$ takes a simple and explicit {\it canonical} form. Some variations are also discussed. Keywords: nverse optimization; positivity certificate; mathematical programming; global optimization; semidefinite programming Category 1: Global Optimization (Theory ) Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 3: Other Topics (Other ) Citation: Download: [PDF]Entry Submitted: 03/21/2011Entry Accepted: 03/21/2011Entry Last Modified: 03/21/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.