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A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs

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Abstract.

We propose a branch-and-bound algorithm for solving nonconvex quadratically-constrained quadratic programs. The algorithm is novel in that branching is done by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles. Explicit formulae for the convex and concave envelopes of bilinear functions over triangles and rectangles are derived and shown to be second-order cone representable. The usefulness of these new relaxations is demonstrated both theoretically and computationally.

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  1. Industrial and Systems Engineering Department, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015, USA

    Jeff Linderoth

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  1. Jeff Linderoth
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Linderoth, J. A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math. Program. 103, 251–282 (2005). https://doi.org/10.1007/s10107-005-0582-7

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