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Objective Function Decomposition in Global Optimization

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Learning and Intelligent Optimization (LION 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10556))

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Abstract

In this paper we consider global optimization problems in which objective functions are explicitly given and can be represented as compositions of some other functions. We discuss an approach of reducing the complexity of the objective by introducing new variables and adding new constraints.

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References

  1. Bromberg, M., Chang, T.C.: A function embedding technique for a class of global optimization problems one-dimensional global optimization. In: Proceedings of the 28th IEEE Conference on Decision and Control, vol. 1–3, pp. 2451–2556 (1989)

    Google Scholar 

  2. Hansen, P., Jaumard, B.: Lipschitz optimization. In: Pardalos, P.M., Horst, R. (eds.) Handbook of Global Optimization, pp. 407–494. Kluwer Academic Publishers, Dordrecht (1995)

    Chapter  Google Scholar 

  3. Hansen, P., Jaumard, B., Lu, S.H.: An analytical approach to global optimization. Math. Program. 52(1), 227–254 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hamed, A.S.E.-D., McCormick, G.P.: Calculations of bounds on variables satisfying nonlinear equality constraints. J. Glob. Optim. 3, 25–48 (1993)

    Article  MATH  Google Scholar 

  5. Horst, R., Thoai, N.V.: Utility functions programs and optimization over efficient set in multiple-objective decision making. JOTA 92(3), 605–631 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches. Springer, Heidelberg (1996). doi:10.1007/978-3-662-03199-5

    Book  MATH  Google Scholar 

  7. McCormick, G.P.: Attempts to calculate global solution of problems that may have local minima. In: Lootsma, F. (ed.) Numerical Methods for Nonlinear Optimization, pp. 209–221. Academic Press, London, New York (1972)

    Google Scholar 

  8. Pardalos, P.M.: An open global optimization problem on the unit sphere. J. Glob. Optim. 6, 213 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pardalos, P.M., Shalloway, D., Xue, G.: Optimization methods for computing global minima of nonconvex potential energy functions. J. Glob. Optim. 4, 117–133 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Paulavičius, R., Žilinskas, J.: Simplicial Global Optimization. Springer Briefs in Optimization. Springer, New York (2014). doi:10.1007/978-1-4614-9093-7

    Book  MATH  Google Scholar 

  11. Pinter, J.: Global Optimization in Action. Kluwer Academic Publishers, Dordrecht (1996)

    Book  MATH  Google Scholar 

  12. Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer Briefs in Optimization. Springer, New York (2013). doi:10.1007/978-1-4614-8042-6

    Book  MATH  Google Scholar 

  13. Sniedovich, M., Macalalag, E., Findlay, S.: The simplex method as a global optimizer: a C-programming perspectuve. J. Glob. Optim. 4, 89–109 (1994)

    Article  MATH  Google Scholar 

  14. Strekalovsky, A.S.: On solving optimization problems with hidden nonconvex structures. In: Rassias, T.M., Floudas, C.A., Butenko, S. (eds.) Optimization in Science and Engineering, pp. 465–502. Springer, New York (2014). doi:10.1007/978-1-4939-0808-0_23

    Chapter  Google Scholar 

  15. Strongin, R.G., Sergeev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  16. Tuy, H.: D.C. optimization: theory, methods and algorithms. In: Pardalos, P.M., Horst, R. (eds.) Handbook of Global Optimization, pp. 149–216. Kluwer Academic Publishers, Dordrecht (1995)

    Chapter  Google Scholar 

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Acknowledgments

This work is supported by the RFBR grant number 15-07-08986.

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Authors and Affiliations

  1. Melentiev Energy Systems Institute SB RAS, Lermontov, Russia

    Oleg V. Khamisov

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  1. Oleg V. Khamisov
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Correspondence to Oleg V. Khamisov .

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Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

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Khamisov, O.V. (2017). Objective Function Decomposition in Global Optimization. In: Battiti, R., Kvasov, D., Sergeyev, Y. (eds) Learning and Intelligent Optimization. LION 2017. Lecture Notes in Computer Science(), vol 10556. Springer, Cham. https://doi.org/10.1007/978-3-319-69404-7_28

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  • DOI: https://doi.org/10.1007/978-3-319-69404-7_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69403-0

  • Online ISBN: 978-3-319-69404-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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