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A study of rank-one sets with linear side constraints and application to the pooling problem

Santanu S. Dey(santanu.dey***at***isye.gatech.edu)
Burak Kocuk(burakkocuk***at***sabanciuniv.edu)
Asteroide Santana(asteroide.santana***at***gatech.edu)

Abstract: We study sets defined as the intersection of a rank-1 constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-1 set is polyhedral or second-order cone representable. In all these cases, we also show that a linear objective can be optimized in polynomial time over these sets. Towards the application side, we show how these sets relate to commonly occurring substructures of a general quadratically constrained quadratic program. To further illustrate the benefit of studying quadratically constrained quadratic programs from a rank-1 perspective, we propose new rank-1 formulations for the generalized pooling problem and use our convexification results to obtain several new convex relaxations for the pooling problem. Finally, we run a comprehensive set of computational experiments and show that our convexification results together with discretization significantly help in improving dual bounds for the generalized pooling problem.

Keywords: quadratically constrained quadratic program; convex relaxation; second-order cone representable; pooling problem; discretization

Category 1: Applications -- Science and Engineering

Category 2: Global Optimization


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Entry Submitted: 02/02/2019
Entry Accepted: 02/02/2019
Entry Last Modified: 02/02/2019

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