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On KKT Points of Homogeneous Programs

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Abstract

Homogeneous programming is an important class of optimization problems. The purpose of this note is to give a truly equivalent characterization of KKT points of homogeneous programming problems, correcting a result given by Lasserre and Hiriart-Urruty in Ref. 1.

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References

  1. Lasserre, J. B., and Hiriart-Urruty, J., Mathematical Properties of Optimization Problems Defined by Positivity Homogeneous Functions, Journal of Optimization Theory and Applications, Vol. 112, pp. 31–52, 2002.

    Article  MathSciNet  Google Scholar 

  2. Vandenberghe, L., and Boyd, S., Semidefinite Programming, SIAM Review, Vol. 38, pp. 49–95, 1996.

    Article  MathSciNet  Google Scholar 

  3. Glassey, C. R., Explicit Duality for Convex Homogeneous Programs, Mathematical Programming, Vol. 10, pp. 176–191, 1976.

    Article  MathSciNet  Google Scholar 

  4. Ye, Y., Semidefinite Programming for Global Quadratic Optimization, Proceedings of the 5th International Conference on Optimization Techniques and Applications, Hong Kong, 2001; Edited by D. Li, Vol. 4, pp. 1826–1833, 2001.

    Google Scholar 

  5. Eisenberg, E., Duality in Homogeneous Programming, Proceedings of the American Mathematical Society, Vol. 12, pp. 783–787, 1961.

    Article  MathSciNet  Google Scholar 

  6. Rubinov, A. M., and Glover, B. M., Characterizations of Optimality for Homogeneous Programming Problems with Applications, Recent Advances in Nonsmooth Optimization, World Science Publishers, River Edge, New Jersey, 1995, pp. 351–380.

    Google Scholar 

  7. Gwinner, J., An Extension Lemma and Homogeneous Programming, Journal of Optimization Theory and Applications, Vol. 47, pp. 321–336, 1985.

    Article  MathSciNet  Google Scholar 

  8. Gwinner, J., Results of Farkas Type, Numerical Functional Analysis and Optimization, Vol. 9, pp. 471–520, 1987.

    MathSciNet  Google Scholar 

  9. Bagirov, A. M., and Rubinov, A. M., Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex, Annals of Operations Research, Vol. 98, pp. 171–187, 2000.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Y. B. Zhao (Associate Professor)

  2. Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, NT, Hong Kong

    D. Li (Professor)

Authors
  1. Y. B. Zhao
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  2. D. Li
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Additional information

Communicated by P. Tseng

This work was partially supported by the National Natural Science Foundation of China, Grants 10201032 and 70221001, and by the Research Grants Council, Hong Kong, Grant CUHK4180/03E.

The authors thank two anonymous referees for valuable remarks and insights that have helped improving the paper.

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Zhao, Y.B., Li, D. On KKT Points of Homogeneous Programs. J Optim Theory Appl 130, 369–376 (2006). https://doi.org/10.1007/s10957-006-9109-5

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  • DOI: https://doi.org/10.1007/s10957-006-9109-5

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