Open AccessBRANCH AND BOUND WITH SIMPLICIAL PARTITIONS FOR GLOBAL OPTIMIZATION
Author(s) -
Julius Žilinskas
Publication year - 2008
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/1392-6292.2008.13.145-159
Subject(s) - mathematics , vertex (graph theory) , branch and bound , combinatorics , homogeneous space , simplicial approximation theorem , combinatorial optimization , triangulation , simplicial manifold , simplicial complex , upper and lower bounds , abstract simplicial complex , global optimization , mathematical optimization , graph , pure mathematics , simplicial set , geometry , mathematical analysis , homotopy , homotopy category
Branch and bound methods for global optimization are considered in this paper. Advantages and disadvantages of simplicial partitions for branch and bound are shown. A new general combinatorial approach for vertex triangulation of hyper‐rectangular feasible regions is presented. Simplicial partitions may be used to vertex triangulate feasible regions of non rectangular shape defined by linear inequality constraints. Linear inequality constraints may be used to avoid symmetries in optimization problems.