Journals / Journal of Multidisciplinary Modeling and Optimization / 2018 / Cilt: 1 Sayı: 2

Smoothing Approximations to Non-smooth Functions

Ahmet Sahiner(SÜLEYMAN DEMİREL ÜNİVERSİTESİ)0000-0002-4945-2476
Nurullah Yilmaz(SÜLEYMAN DEMİREL ÜNİVERSİTESİ)0000-0001-6429-7518
Shehab Ahmed Ibrahem(SÜLEYMAN DEMİREL ÜNİVERSİTESİ)0000-0003-2428-2703
Pages
69–74
Publication Date
2019-01-21
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, some numerical examples are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new smoothing method is proposed for non-smooth functions.
📊
Key Findings & Data:The theoretical results and error estimates are presented about this new smoothing method.
💡
Conclusion & Impact:Finally, some numerical examples are given.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:non-smooth functions · smoothing techniques · non-smooth functions

Abstract

In this study, a new smoothing method is proposed for non-smooth functions. The theoretical results and error estimates are presented about this new smoothing method. Finally, some numerical examples are given.

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Cite This Article

Sahiner, A., Yilmaz, N., Ibrahem, S. A. (2019). Smoothing Approximations to Non-smooth Functions. Journal of Multidisciplinary Modeling and Optimization, Cilt: 1 Sayı: 2, 69–74. https://ajindex.com/articles/1593128

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References (22)

  1. R. T. Rockafellar, R. J-B. Wets R. J-B., Variational Analysis, Springer, Berlin, 1998.
  2. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
  3. V. F. Demyanov, A. M. Rubinov, Constructive Nonsmooth Analysis. Verlag Peter Lang, Frankfurt, 1995.
  4. B. Akteke-Ozkurt, G. W. Weber, G. Koksal, Optimization of generalized desirability functions under model uncertainty, Optimization, 66 (12) 2017, 2157--2169.
  5. A. Sahiner, N. Yilmaz and G. Kapusuz, A novel modeling and smoothing technique in global optimization, J. Ind. Manage. Optim., 15 (1) 2019, 113-130.
  6. D. Bertsekas, Nondifferentiable optimization via approximation, Math. Program. Stud., 3 1975, 1--25.
  7. I. Zang, A smoothing out technique for min-max optimization, Math. Programm., 19 1980, 61--77.
  8. A. E. Xavier, The hyperbolic smoothing clustering method, Patt. Recog., 43 2010, 731--737.
  9. A. M. Bagirov, A. Al Nuamiat and N. Sultanova, Hyperbolic smoothing functions for nonsmooth minimization, Optimization, 62 (6) 2013, 759--782.
  10. M. Jiang, R. Shen, X. Xu, Z. Meng, Second-order smoothing objective penalty function for constrained optimization problems, Numer. Func. Anal. Opt., 35 2014, 294--309.
  11. S. J. Lian Smoothing approximation to $l_1$ exact penalty for inequality constrained optimization, Appl. Math. Comput., 219 2012, 3113--3121.
  12. C. Chen and O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problem, Comput. Optim. Appl., 5 1996, 97--138.
  13. X. Chen and W. Zhou, Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization, SIAM J. Imaging Sciences, 3(4) 2010, 765--790.
  14. G.W. Weber, I. Batmaz and G. Koksal, CMARS: a new contribution to nonparametric regression with multivariate adaptiveregression splines supported by continuous optimization, Inverse. Probl. Eng., 20(3) 2012, 371--400.
  15. P. Taylan, G.-W. Weber, F. Yerlikaya Ozkurt, A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization. TOP 18(2) 2010, 377--395.
  16. A. Sahiner, N. Yilmaz and G. Kapusuz, A new global optimization method and applications, Carpathian Math. J., 33(3) 2017, 373-380.
  17. A. Sahiner, S. A. Ibrahem, A new global optimization technique by auxiliary function method in a directional search, Optim. Lett. 2018, doi: 10.1007/s11590-018-1315-1
  18. J. Lee, D. Skipper, Virtuous smoothing for global optimization, J. Glob. Optim., 69(3) 2017, 677-697.
  19. X. Chen, Smoothing methods for nonsmooth, nonconvex minimzation, Math. Program. Ser. B, 134 2012, 71--99.
  20. C. Grossmann, Smoothing techniques for exact penalty function methods, Contemporary Mathematics, 658 2016, 249--265.
  21. F. G. Vazquez, H. Gunzel and J. J. Ruckmann, On logarithmic smoothing of the maximum function, Ann. Oper. Res., 101 2001, 209--220.
  22. H. Th. Jongen and D. Pallaschke, On linearization and continuous selection of functions, Optimization, 19(3) 1988, 343--353.