-

 

 

 




Optimization Online





 

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

Citation:

Download: [PDF]

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

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society