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Optimization of positive generalized polynomials under \(l^p\) constraints. (English) Zbl 0914.90237

Summary: The problem of maximizing a nonnegative 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.

MSC:

90C30 Nonlinear programming
90C25 Convex programming
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