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Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization

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Abstract

We prove a sufficient global optimality condition for the problem of minimizing a quadratic function subject to quadratic equality constraints where the variables are allowed to take values −1 and 1. We extend the condition to quadratic problems with matrix variables and orthonormality constraints, and in particular to the quadratic assignment problem.

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References

  1. Garey, M. R., and Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco, California, 1979.

    Google Scholar 

  2. Beck, A. and Teboulle, M., Global Optimality Conditions for Quadratic with Binary Constraints, SIAM Journal on Optimization, Vol. 11, pp. 179–188, 2000.

    Google Scholar 

  3. Bertsekas, D. P., Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1995; see 2nd Edition, 1999.

    Google Scholar 

  4. Luenberger, D. G., Optimization by Vector Space Methods, John Wiley, New York, NY, 1969.

    Google Scholar 

  5. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.

    Google Scholar 

  6. Nesterov, Y., and Nemirovski, A., Interior-Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, Pennsylvania, 1993.

    Google Scholar 

  7. Hiriart-Urruty, J. B., Conditions for Global Optimality, Handbook for Global Optimization, Kluwer Academic Publishers, Dordrecht, Holland, pp. 1–26, 1999.

    Google Scholar 

  8. Hiriart-Urruty, J. B., Conditions for Global Optimality 2, Journal of Global Optimization, Vol. 13, pp. 349–367, 1998.

    Google Scholar 

  9. Hiriart-Urruty, J. B., Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints, Journal of Global Optimization, Vol. 21, pp. 445–455, 2001.

    Google Scholar 

  10. Carraresi, P., Farinaccio, F., and Malucelli, F., Testing Optimality for Quadratic 0–1 Problems, Mathematical Programming, Vol. 85, pp. 407–421, 1999.

    Google Scholar 

  11. Anstreicher, K., Chen, X., Wolkowicz, H., and Yuan, Y., Strong Duality for a Trust-Region Type Relaxation of the Quadratic Assignment Problem, Linear Algebra and Its Applications, Vol. 301, pp. 121–136, 1999.

    Google Scholar 

  12. Anstreicher, K., and Wolkowicz, H., On Lagrangian Relaxation of Quadratic Matrix Constraints, SIAM Journal on Matrix Analysis and Applications, Vol. 22, pp. 41–55, 2000.

    Google Scholar 

  13. Anstreicher, K., Eigenvalue Bounds versus Semide nite Relaxations for the Quadratic Assignment Problem, Technical Report, University of Iowa, Iowa City, Iowa, 1999.

    Google Scholar 

  14. Anstreicher, K., and Brixius, N. W., A New Bound for the Quadratic Assignment Problem Based on Convex Quadratic Programming, Mathematical Programming, Vol. 89, pp. 341–357, 2001.

    Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, Bilkent University, Bilkent, Ankara, Turkey

    M. Ç. Pinar (Associate Professor)

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  1. M. Ç. Pinar
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Pinar, M.Ç. Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization. Journal of Optimization Theory and Applications 122, 433–440 (2004). https://doi.org/10.1023/B:JOTA.0000042530.24671.80

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  • DOI: https://doi.org/10.1023/B:JOTA.0000042530.24671.80

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