Non-Convex Quadratic Optimization

This video shows one of the major new feature in Gurobi 9.0, the new bilinear solver, which allows users to solve problems with non-convex quadratic objectives and constraints such as QPs, QCPs, MIQPs, and MIQCPs.

Webinar Summary

One major new feature in Gurobi 9.0 is a new bilinear solver, which allows users to solve problems with non-convex quadratic objectives and constraints (i.e., QPs, QCPs, MIQPs, and MIQCPs). Many non-linear optimization solvers search for locally optimal solutions to these problems.

In contrast, Gurobi can now solve these problems to global optimality. Non-convex quadratic optimization problems arise in various industrial applications. In particular, non-convex quadratic constraints are vital to solve classical pooling and blending problems.

In this webinar session, we will:

  • Introduce MIQCPs and mixed-integer bilinear programming
  • Discuss algorithmic ideas for handling bilinear constraints
  • Show a live demo of how Gurobi 9.0 supports bilinear constraints by building and solving a small instance of the pooling problem

Presenters

Dr. Tobias Achterberg

Dr. Tobias Achterberg, Director of Development at Gurobi Optimization. Dr. Achterberg studied mathematics and computer science at the Technical University of Berlin and the Zuse Institute Berlin. He finished his Ph.D. in mathematics under the supervision of Prof. Martin Grötschel in 2007. Dr. Achterberg is the author of SCIP, currently the best academic MIP solver. In addition to numerous publications in scientific journals, he has also received several awards for his dissertation and for SCIP, such as the Beale-Orchard-Hays Prize. From 2006, Dr. Achterberg worked for ILOG / IBM as a developer of CPLEX in versions 11 to 12.6. Since 2014, he has been involved as a Senior Developer in the development of the Gurobi Optimizer.

 

 Dr. Eli Towle has a Ph.D. in Industrial and Systems Engineering from the University of Wisconsin – Madison. His  research focused on stochastic network interdiction problems with applications to nuclear weapons smuggling.  He also explored the theory for improving  relaxations for a broad class of nonconvex optimization problems.

 

 

 

Presented Materials

You can download the PDF with the slides here and the pooling problem Jupyter Notebook here.