A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms
 Juan M. Zamora,
 Ignacio E. Grossmann
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A new deterministic branch and bound algorithm is presented in this paper for the global optimization of continuous problems that involve concave univariate, bilinear and linear fractional terms. The proposed algorithm, the branch and contract algorithm, relies on the use of a boundscontraction subproblem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values above a known upper bound. The solution of contraction subproblems at selected branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solution tree. The use of the proposed algorithm is illustrated with several numerical examples.
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 Title
 A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms
 Journal

Journal of Global Optimization
Volume 14, Issue 3 , pp 217249
 Cover Date
 19990501
 DOI
 10.1023/A:1008312714792
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Bilinear terms
 Bounds contraction
 Branch and contract
 Concave separable functions
 Continuous global optimization
 Linear fractional terms
 Industry Sectors
 Authors

 Juan M. Zamora ^{(1)}
 Ignacio E. Grossmann ^{(1)}
 Author Affiliations

 1. Department of Chemical Engineering, Carnegie Mellon University Pittsburgh, PA, 152133890, USA