Abstract
We consider the problem of maximizing a quadratic function on the set { −1, l}n. This problem is related to some graph partitioning problems. We propose a path following method to compute an upper bound to the previous maximization problem. Numerical implementation of the proposed method and related numerical experience are presented.
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References
Garey, M.R., Johnson, D.S., “Computers and Intractability: A Guide to the Theory of NP-Completeness,” W.H. Freeman, San Francisco, 1979.
Garey, M.R., Johnson, D.S., Stockmejer, L., “Some Simplified NP complete Graph Problems,” Theoretical Computer Science 1, 1976, pp. 237 - 267.
Pardalos, P.M., Wolkowicz, H., “Quadratic Assignment and Related Problems,” DIM ACS Series, American Mathematical Society 16, 1994.
Pardalos, P.M., Phillips, A.T., Rosen, J.B.,“Topics in Parallel Computing in Mathematical Programming,” Science Press, 1992.
Zirilli, F., “The Use of Ordinary Differential Equations in the Solution of Non Linear Systems of Equations,” Nonlinear Optimization, 19S1, M.T.D. Powell, Ed., Academic Press, New York. 19S2, pp. 39–7.
Kamath, A., Karmarkar, N., “A Continuous Approach to Compute Upper Bound in Quadratic Maximization Problems with Integer Constraints,” Recent Advances in Global Optimization, C.A. Floudas and P.M. Pardalos, Eds., Princeton University Press, Princeton N.J. ( USA ), 1991, pp. 125–140.
Herzel, S., Recchioni, M.C., Zirilli, F.,“ A Quadraticaliy Convergent Method for Linear Programming, ” Linear Algebra and Its Appl., 152, 1991, pp. 255–289.
Pardalos, P.M .,“Construction of Test Problems in Quadratic Bivalent Programming,” ACM Transactions on Mathematical Software 17, 1991, pp.74–87.
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© 1996 Kluwer Academic Publishers
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Maponi, P., Recchioni, M.C., Zirilli, F. (1996). The Use of Ordinary Differential Equations in Quadratic Maximization with Integer Constraints. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_8
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DOI: https://doi.org/10.1007/978-1-4613-3437-8_8
Publisher Name: Springer, Boston, MA
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Online ISBN: 978-1-4613-3437-8
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