A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs

Authors:
Ulrich Raber
Affiliations:
Department of Mathematics, University of Trier, Trier, Germany
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

In this paper we present an algorithm for solving nonconvexquadratically constrained quadratic programs (all-quadratic programs). Themethod is based on a simplicial branch-and-bound scheme involving mainlylinear programming subproblems. Under the assumption that a feasible pointof the all-quadratic program is known, the algorithm guarantees anϵ-approximate optimal solution in a finite number ofiterations. Computational experiments with an implementation of theprocedure are reported on randomly generated test problems. The presentedalgorithm often outperforms a comparable rectangular branch-and-bound method.