Abstract

The problem of maximizing a non-negative generalized polynomial of degree at most pp on the lpl_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.

Author information

Contact details are reproduced from the original publication and may be historical.

Laurent Baratchart

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

Marc Berthod

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

Loïc Pottier

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

Keywords

  • constrained optimization
  • convex optimization
  • combinatorial optimization
  • subhomogeneous functions
  • labeling

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Suggested citation

L. Baratchart, M. Berthod, L. Pottier. “Optimization of Positive Generalized Polynomials Under l^p Constraints.” Journal of Convex Analysis 5 (1998), No. 2, 353–379. https://doi.org/10.68381/jca05-23

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Published by Heldermann Verlag, 1998. Rights now held by Banach Press.