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Solving Mixed-Integer Nonlinear Programs by QP-Diving

Ashutosh Mahajan(mahajan***at***mcs.anl.gov)
Sven Leyffer(leyffer***at***mcs.anl.gov)
Christian Kirches(christian.kirches***at***iwr.uni-heidelberg.de)

Abstract: We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branch-and-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on a range of test problems. Our numerical experience shows that the new algorithm allows us to exploit warm-starting techniques from quadratic programming, resulting in a reduction in solve times for convex MINLPs by orders of magnitude on some classes of problems.

Keywords: Mixed-Integer Nonlinear Programming, Sequential Quadratic Programming, Branch-and-Bound

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: Technical Report ANL/MCS-P2071-0312, Argonne National Laboratory, March, 2012.

Download: [PDF]

Entry Submitted: 03/26/2012
Entry Accepted: 03/27/2012
Entry Last Modified: 03/26/2012

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