Abstract
Consider one of the simplest on formulation problem of nonconvex polynomial programming: find infinum ρ * (A) of
where A is an arbitrary symmetric matrix n × n, A = {a ij } n i ,j =1. ρ * (A) may accept only two values: 0 or − ∞. If ρ * (A) = 0, then x* = 0 is the optimal point of the problem (9.1). It is known that class of the problems: “ρ * (A)= 0? ” for arbitrary integer (rational) symmetric matrices A of arbitrary size n × n is NP-complete (see [GJ 79]. Note that for convex K(x) the answer is trivial: ρ * (A) = 0.
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© 1998 Springer Science+Business Media Dordrecht
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Shor, N.Z. (1998). Global Minimization of Polynomial Functions and 17-th Hilbert Problem. In: Nondifferentiable Optimization and Polynomial Problems. Nonconvex Optimization and Its Applications, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6015-6_9
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DOI: https://doi.org/10.1007/978-1-4757-6015-6_9
Publisher Name: Springer, Boston, MA
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