caa a22 4500 465774326 CHVBK 20180323111937.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02283689 doi (NATIONALLICENCE)springer-10.1007/BF02283689 A parallel algorithm for partially separable non-convex global minimization: Linear constraints [Elektronische Daten] [A. Phillips, J. Rosen] The global minimization of large-scale partially separable non-convex problems over a bounded polyhedral set using a parallel branch and bound approach is considered. The objective function consists of a separable concave part, an unseparated convex part, and a strictly linear part, which are all coupled by the linear constraints. These large-scale problems are characterized by having the number of linear variables much greater than the number of nonlinear variables. An important special class of problems which can be reduced to this form are the synomial global minimization problems. Such problems often arise in engineering design, and previous computational methods for such problems have been limited to the convex posynomial case. In the current work, a convex underestimating function to the objective function is easily constructed and minimized over the feasible domain to get both upper and lower bounds on the global minimum function value. At each minor iteration of the algorithm, the feasible domain is divided into subregions and convex underestimating problems over each subregion are solved in parallel. Branch and bound techniques can then be used to eliminate parts of the feasible domain from consideration and improve the upper and lower bounds. It is shown that the algorithm guarantees that a solution is obtained to within any specified tolerance in a finite number of steps. Computational results obtained on the four processor Cray 2, both sequentially and in parallel on all four processors, are also presented. J.C. Baltzer A.G. Scientific Publishing Company, 1990 Global minimization nationallicence non-convex programming nationallicence parallel algorithms nationallicence Phillips A. Computer Science Department, United States Naval Academy, 21402, Annapolis, MD, USA aut Rosen J. Computer Science Department, University of Minnesota, 55455, Minneapolis, MN, USA aut Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 101-118 0254-5330 25:1<101 1990 25 10479 https://doi.org/10.1007/BF02283689 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02283689 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Phillips A. Computer Science Department, United States Naval Academy, 21402, Annapolis, MD, USA aut NATIONALLICENCE 700 1- Rosen J. Computer Science Department, University of Minnesota, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 101-118 0254-5330 25:1<101 1990 25 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer