Global optimization over general compact sets by the beta algorithm: A MAPLE code

Authors:
M. Delgado Pineda;E. A. Galperin
Affiliations:
Departamento de Matemáticas Fundamentales Universidad de Educación a Distancia Facultad de Ciencias c/ Senda del Rey 9, C.P. 28040 Madrid, Spain;Départament de Mathématiques et d'Informatique Université du Québec à Montréal, C.P. 8888, Suce. Centre Ville Montréal, Québec H3C 3P8, Canada
Venue:
Computers & Mathematics with Applications
Year:
2006

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Abstract

A variant of the beta algorithm based on the cubic algorithm [1,2] is presented for global optimization of Holder continuous functions over general compact sets. The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]^n universal for all problems. On this basis, a MAPLE code of modular structure is developed for full global optimization of functions of n variables. The code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. The code is ready for engineering applications. Results of numerical experiments are presented, with graphs, to illustrate the use of the code.