Integer and combinatorial optimization
Integer and combinatorial optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Journal of Global Optimization
Relaxations of multilinear convex envelopes: dual is better than primal
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
On valid inequalities for quadratic programming with continuous variables and binary indicators
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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The pooling problem consists of finding the optimal quantity of final products to obtain by blending different compositions of raw materials in pools. Bilinear terms are required to model the quality of products in the pools, making the pooling problem a non-convex continuous optimization problem. In this paper we study a generalization of the standard pooling problem where binary variables are used to model fixed costs associated with using a raw material in a pool. We derive four classes of strong valid inequalities for the problem and demonstrate that the inequalities dominate classic flow cover inequalities. The inequalities can be separated in polynomial time. Computational results are reported that demonstrate the utility of the inequalities when used in a global optimization solver.