Friday, November 18, 2005
1:30 pm Posner Hall 259
Pierre Bonami
Post Doctoral Fellow in OPS Research
Tepper School of Business, Carnegie Mellon
An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
We present our work in an on-going project with the Chemical Engineering Department and IBM to build new open source software for solving Mixed Integer Non Linear Programs.
We address the general problem of minimizing a twice differentiable convex function in a region described by convex constraints with integrality requirements on some of the variables.
In particular we present an hybrid algorithm that combines non-linear and linear relaxations of MINLPs in a branch-and-cut framework. This flexible algorithm is implemented in the COIN-OR framework using Cbc (a branch-and-cut algorithm), Ipopt (an interior point solver for nonlinear programming) and Clp (a linear programming solver) as building blocks. We present computational results comparing this hybrid algorithm to commercial solvers, and our implementations of branch-and-bound, and outer approximation algorithms. The algorithms are compared on a new publicly available library of convex mixed integer nonlinear programs that we have put together.
