Journal of Convex Analysis, Vol. 5, No. 2, pp. 353-379 (1998)

Optimization of Positive Generalized Polynomials under $ \boldsymbol{l^p}$ Constraints

L. Baratchart and M. Berthod and L. Pottier

Inria-Sophia Antipolis, 2004 Route des Lucioles, BP 109 - 06561 Valbonne Cedex, France,

Abstract: The problem of maximizing a non-negative generalized polynomial of degree at most $p$ on the $l_p$-sphere is shown to be equivalent to a concave one. Arguments where the maximum is attained are characterized in connection with the irreducible decomposition of the polynomial, and an application to the labelling problem is presented where these results are used to select the initial guess of a continuation method.

Keywords: constrained optimization, convex optimization, combinatorial optimization, subhomogeneous functions, labeling

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