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A penalty for concave minimization derived from the tuy cutting plane
Author(s) -
Bretthauer Kurt M.
Publication year - 1994
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199404)41:3<455::aid-nav3220410310>3.0.co;2-q
Subject(s) - cutting plane method , penalty method , branch and bound , mathematical optimization , minification , linear programming , mathematics , integer programming , plane (geometry) , function (biology) , upper and lower bounds , concave function , variety (cybernetics) , nonlinear programming , branch and cut , nonlinear system , statistics , geometry , mathematical analysis , physics , quantum mechanics , evolutionary biology , regular polygon , biology
A wide variety of optimization problems have been approached with branch‐and‐bound methodology, most notably integer programming and continuous nonconvex programming. Penalty calculations provide a means to reduce the number of subproblems solved during the branch‐and‐bound search. We develop a new penalty based on the Tuy cutting plane for the nonconvex problem of globally minimizing a concave function over linear constraints and continuous variables. Computational testing with a branch‐and‐bound algorithm for concave minimization indicates that, for the problems solved, the penalty reduces solution time by a factor ranging from 1.2 to 7.2. © 1994 John Wiley & Sons, Inc.