Titlebook: Nondifferentiable Optimization and Polynomial Problems; Naum Z. Shor Book 1998 Springer Science+Business Media Dordrecht 1998 Mathematica.

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Nondifferentiable Optimization and Polynomial Problems978-1-4757-6015-6Series ISSN 1571-568X

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https://doi.org/10.1007/978-1-4757-6015-6Mathematica; algebra; algorithms; calculus; complexity; graph theory; optimization; programming; combinatori

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Elements of Information and Numerical Complexity of Polynomial Extremal Problems,ources studying an arbitrary algorithm that solves the given problem. But to get an answer for the question of how good a particular algorithm is we must find the lower bounds for computational resources, the limits that cannot be improved by the “best” algorithm among the potentially possible ones.

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Book 1998 with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef‘; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x

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1571-568X e is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a P