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Strong Convex Nonlinear Relaxations of the Pooling Problem: Extreme Points

Please always quote using this URN: urn:nbn:de:0297-zib-67801
  • We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which products are mixed in intermediate pools in order to meet quality targets at their destinations. In this technical report, we characterize the extreme points of the convex hull of our non-convex set, and show that they are not finite, i.e., the convex hull is not polyhedral. This analysis was used to derive valid nonlinear convex inequalities and show that, for a specific case, they characterize the convex hull of our set. The new valid inequalities and computational results are presented in ZIB Report 18-12.

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Author:James Luedtke, Claudia D'Ambrosio, Jeff Linderoth, Jonas SchweigerORCiD
Document Type:ZIB-Report
Tag:Extreme Points; Pooling Problem; Relaxation
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C20 Quadratic programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C26 Nonconvex programming, global optimization
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C35 Programming involving graphs or networks [See also 90C27]
Date of first Publication:2018/03/08
Series (Serial Number):ZIB-Report (18-13)
ISSN:1438-0064