Abstract
In this paper we present an algorithm for solving nonconvex quadratically constrained quadratic programs (all-quadratic programs). The method is based on a simplicial branch-and-bound scheme involving mainly linear programming subproblems. Under the assumption that a feasible point of the all-quadratic program is known, the algorithm guarantees an ε-approximate optimal solution in a finite number of iterations. Computational experiments with an implementation of the procedure are reported on randomly generated test problems. The presented algorithm often outperforms a comparable rectangular branch-and-bound method.
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Raber, U. A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs. Journal of Global Optimization 13, 417–432 (1998). https://doi.org/10.1023/A:1008377529330
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DOI: https://doi.org/10.1023/A:1008377529330