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Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex

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  • A.M. Bagirov
  • A.M. Rubinov

Abstract

In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • A.M. Bagirov & A.M. Rubinov, 2000. "Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex," Annals of Operations Research, Springer, vol. 98(1), pages 171-187, December.
    • Handle: RePEc:spr:annopr:v:98:y:2000:i:1:p:171-187:10.1023/a:1019204407420
    DOI: 10.1023/A:1019204407420
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    Citations

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    Cited by:

    1. Rubinov, A.M. & Soukhorokova, N.V. & Ugon, J., 2006. "Classes and clusters in data analysis," European Journal of Operational Research, Elsevier, vol. 173(3), pages 849-865, September.
    2. Y. B. Zhao & D. Li, 2006. "On KKT Points of Homogeneous Programs," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 369-376, August.
    3. A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
    4. de Klerk, E. & den Hertog, D. & Elfadul, G.E.E., 2005. "On the Complexity of Optimization over the Standard Simplex," Other publications TiSEM 3789955a-6533-4a4e-aca2-6, Tilburg University, School of Economics and Management.
    5. de Klerk, E. & den Hertog, D. & Elabwabi, G., 2008. "On the complexity of optimization over the standard simplex," European Journal of Operational Research, Elsevier, vol. 191(3), pages 773-785, December.
    6. Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
    7. A. Ferrer & M. A. Goberna & E. González-Gutiérrez & M. I. Todorov, 2017. "A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem," Annals of Operations Research, Springer, vol. 258(2), pages 587-612, November.

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