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A dynamic programming method for building free algebras

✍ Scribed by Irvin Roy Hentzel; David Pokrass Jacobs

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
437 KB
Volume
22
Category
Article
ISSN
0898-1221

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✦ Synopsis

Abstract~We are interested in deciding if a given nonmmociative polynomial h is an identity for a variety of nonauociative algebras. We present an algorithm for constructing a certain homomorphic image of a free nonMsoclative algebra which is suflident to answer the question. The algorithm resembles dy~am;c programming in that the algebra is built by constructing a sequence of subspaces; the ba~ of each subspace is determined by the basis of previous subspaces. The number of arithmetic operations required to construct the algebra is bounded by a polynomial in the degree of h and the dimension of the resulting algebra.

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In this paper, we consider the box constrained nonlinear integer programming problem. We present an auxiliary function, which has the same discrete global minimizers as the problem. The minimization of the function using a discrete local search method can escape successfully from previously converge