A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs
J Linderoth - Mathematical programming, 2005 - Springer
Mathematical programming, 2005•Springer
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.
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.
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.
Springer
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