parsimony-inducing norms

Thursday, January 28, 2016 - 9:00am - 9:50am
Jean Lasserre (Centre National de la Recherche Scientifique (CNRS))
We consider the family of nonnegative homogeneous polynomials of even degree p whose sublevel set G = {x : g(x) ≤ 1} (a unit ball) has same fixed volume and want to find in this family the one that minimizes either the parsimony-inducing ell_1-norm or the ell_2-norm of its vector of coefficients. We first show that in both cases this is a convex optimization problem with a unique optimal solution. In the former case, the unique solution is the polynomial associated with the L_p-ball, thus recovering a parsimony property of its representation via ell_1-minimization.
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