caa a22 4500 465774490 CHVBK 20180323111938.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02283695 doi (NATIONALLICENCE)springer-10.1007/BF02283695 An explicit characterization of the convex envelope of a bivariate bilinear function over special polytopes [Elektronische Daten] [Hanif Sherali, Amine Alameddine] In this paper, we constructively derive an explicit characterization of the convex envelope of a bilinear function over a special type of polytope in ℝ2. Our motivation stems from the use of such functions for deriving strengthened lower bounds within the context of a branch-and-bound algorithm for solving bilinear programming problems. For the case of polytopes with no edges having finite positive slopes, that is polytopes with "downward” sloping edges (which we call D-polytopes), we obtain a direct, explicit characterization of the convex envelope. This case subsumes the analysis of Al-Khayyal and Falk (1983) for constructing the convex envelope of a bilinear function over a rectangle in ℝ2. For non-D-polytopes, the analysis is more complex. We propose three strategies for this case based on (i) encasing the region in a D-polytope, (ii) employing a discretization technique, and (iii) providing an explicit characterization over a triangle along with a triangular decomposition approach. The analysis is illustrated using numerical examples. J.C. Baltzer A.G. Scientific Publishing Company, 1990 Convex envelopes nationallicence bilinear functions nationallicence bilinear programming problems nationallicence global optimization nationallicence Sherali Hanif Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, 24061-0118, Blacksburg, Virginia, USA aut Alameddine Amine Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, 24061-0118, Blacksburg, Virginia, USA aut Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 197-209 0254-5330 25:1<197 1990 25 10479 https://doi.org/10.1007/BF02283695 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02283695 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sherali Hanif Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, 24061-0118, Blacksburg, Virginia, USA aut NATIONALLICENCE 700 1- Alameddine Amine Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, 24061-0118, Blacksburg, Virginia, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 25/1(1990-12-01), 197-209 0254-5330 25:1<197 1990 25 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer