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Heuristic Pattern Search for Bound Constrained Minimax Problems

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Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6784))

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Abstract

This paper presents a pattern search algorithm and its hybridization with a random descent search for solving bound constrained minimax problems. The herein proposed heuristic pattern search method combines the Hooke and Jeeves (HJ) pattern and exploratory moves with a randomly generated approximate descent direction. Two versions of the heuristic algorithm have been applied to several benchmark minimax problems and compared with the original HJ pattern search algorithm.

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References

  1. Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1999)

    MATH  Google Scholar 

  2. Di Pillo, G., Grippo, L.: A smooth method for the finite minimax problem. Mathematical Programming 60, 187–214 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Mathematical Programming 91, 201–213 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fourer, R., Gay, D.M., Kernighan, B.: A modeling language for mathematical programing. Management Science 36, 519–554 (1990), http://www.ampl.com

    Article  MATH  Google Scholar 

  5. Hedar, A.-R., Fukushima, M.: Heuristic pattern search and its hybridization with simulated annealing for nonlinear global optimization. Optimization Methods and Software 19, 291–308 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. Journal on Associated Computation 8, 212–229 (1961)

    MATH  Google Scholar 

  7. Laskari, E.C., Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization for minimax problems. In: Proceedings of IEEE 2002 Congress on Evolutionary Computation, pp. 1576–1581 (2001) ISBN: 0-7803-7278-6

    Google Scholar 

  8. Lewis, R.M., Torczon, V.: Pattern search algorithms for bound constrained minimization. SIAM Journal on Optimization 9, 1082–1099 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lewis, R.M., Torczon, V.: A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM Journal on Optimization 12, 1075–1089 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liuzzi, G., Lucidi, S., Sciandrone, M.: A derivative-free algorithm for linearly constrained finite minimax problems. SIAM Journal on Optimization 16, 1054–1075 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lukšan, L., Vlček, J.: Test problems for nonsmooth unconstrained and linearly constrained optimization. TR 798, ICS, Academy of Science of the Czech Republic (January 2000)

    Google Scholar 

  12. Parsopoulos, K.E., Vrahatis, M.N.: Unified particle swarm optimization for tackling operations research problems. In: Proceedings of IEEE 2005 Swarm Intelligence Symposium, Pasadena, USA, pp. 53–59 (2005)

    Google Scholar 

  13. Petalas, Y.G., Parsopoulos, K.E., Vrahatis, M.N.: Memetic particle swarm optimization. Annals of Operations Research 156, 99–127 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Polak, E., Royset, J.O., Womersley, R.S.: Algorithms with adaptive smoothing for finite minimax problems. Journal of Optimization Theory and Applications 119, 459–484 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tahk, M.-J., Woo, H.-W., Park, M.-S.: A hybrid optimization method of evolutionary and gradient search. Engineering Optimization 39, 87–104 (2007)

    Article  MathSciNet  Google Scholar 

  16. Torczon, V.: On the convergence of pattern search algorithms. SIAM Journal on Optimization 7, 1–25 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Xu, S.: Smoothing method for minimax problems. Computational Optimization and Applications 20, 267–279 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ye, F., Liu, H., Zhou, S., Liu, S.: A smoothing trust-region Newton-CG method for minimax problem. Applied Mathmatics and Computation 199, 581–589 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhu, Z., Cai, X., Jian, J.: An improved SQP algorithm for solving minimax problems. Applied Mathmatics Letters 22, 464–469 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Algoritmi R & D Centre, University of Minho, 4710-057, Braga, Portugal

    Isabel A. C. P. Espírito Santo & Edite M. G. P. Fernandes

Authors
  1. Isabel A. C. P. Espírito Santo
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  2. Edite M. G. P. Fernandes
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Editor information

Editors and Affiliations

  1. L.I.S.U.T. - D.A.P.I.T., Basilicata University Potenza, 10, Viale dell’Ateneo Lucano, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

  3. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, C.P. 39005, Santander, Spain

    Andrés Iglesias

  4. School of Business Systems, Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  5. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashi-ku, 813-8503, Fukuoka, Japan

    Bernady O. Apduhan

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© 2011 Springer-Verlag Berlin Heidelberg

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Santo, I.A.C.P.E., Fernandes, E.M.G.P. (2011). Heuristic Pattern Search for Bound Constrained Minimax Problems. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21931-3_15

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  • DOI: https://doi.org/10.1007/978-3-642-21931-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21930-6

  • Online ISBN: 978-3-642-21931-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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