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New Underestimator for Univariate Global Optimization

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Modelling, Computation and Optimization in Information Systems and Management Sciences

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 359))

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Abstract

The aim of this paper is to propose a new underestimator for solving univariate global optimization problems, which is better than the underestimator used in the classical αBB method [1], and the quadratic underestimator developed in [4]. We can propose an efficient algorithm based on Branch and Bound techniques and an efficient w-subdivision for branching. A convex/concave test is added to accelerate the convergence of the algorithm.

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References

  1. Androulakis, I.P., Marinas, C.D., Floudas, C.A.: αBB: A global optimization method for general constrained nonconvex problems. J. Glob. Optim. 7, 337–363 (1995)

    Article  MATH  Google Scholar 

  2. de Boor, C.: A practical method Guide to Splines. Applied Mathematical Sciences. Springer (1978)

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  3. Floudas, C.A., Gounaris, C.E.: A review of recent advances in global optimization. Journal of Global Optimization 45, 3–38 (2009)

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  4. Le Thi, H.A., Ouanes, M.: Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint. RAIRO Oper. Res. 40, 285–302 (2006)

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  5. Ouanes, M., Le Thi, H.A., Nguyen, T.P., Zidna, A.: New quadratic lower bound for multivariate functions in global optimization. Mathematics and Computers in Simulation 109, 197–211 (2015)

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Author information

Authors and Affiliations

  1. Laromad, Département de Mathématiques, Faculté des Sciences, Université de Tizi-Ouzou, Tizi Ouzou, Algérie

    Mohand Ouanes

  2. Laboratoire d’Informatique Théorique et Appliquée, Université de Lorraine, Ile du Saulcy, 57045, Metz, France

    Hoai An Le Thi & Ahmed Zidna

Authors
  1. Mohand Ouanes
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  2. Hoai An Le Thi
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  3. Ahmed Zidna
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Corresponding author

Correspondence to Mohand Ouanes .

Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, University of Lorraine-Metz, Metz, France

    Hoai An Le Thi

  2. Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, Rouen, France

    Tao Pham Dinh

  3. Division of Knowledge Management Systems Institute of Informatics (I-32), Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

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Ouanes, M., Le Thi, H.A., Zidna, A. (2015). New Underestimator for Univariate Global Optimization. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_34

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  • DOI: https://doi.org/10.1007/978-3-319-18161-5_34

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18160-8

  • Online ISBN: 978-3-319-18161-5

  • eBook Packages: EngineeringEngineering (R0)

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