New limited memory bundle method for large-scale nonsmooth optimization Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables. In such problems the direct application of smooth gradient-based methods may lead to a failure due to the nonsmooth nature of the problem. On the other hand, none of the current general nonsmooth optimization methods is efficient in large-scale settings. In this article we describe a new limited memory variable metric based bundle method for nonsmooth large-scale optimization. In addition, we introduce a new set of academic test problems for large-scale nonsmooth minimization. Finally, we give some encouraging results from numerical experiments using both academic and practical test problems.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Yuan, Gonglin; Meng, Zehong; Li, Yong: A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations (2016)
  2. Yuan, Gonglin; Wei, Zengxin: A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems (2016)
  3. Curtis, Frank E.; Que, Xiaocun: A quasi-Newton algorithm for nonconvex, nonsmooth optimization with global convergence guarantees (2015)
  4. Karmitsa, Napsu: Diagonal bundle method for nonsmooth sparse optimization (2015)
  5. Bagirov, Adil; Karmitsa, Napsu; Mäkelä, Marko M.: Introduction to nonsmooth optimization. Theory, practice and software (2014)
  6. Burachik, Regina S.; Freire, Wilhelm P.; Kaya, C.Yalçın: Interior epigraph directions method for nonsmooth and nonconvex optimization via generalized augmented Lagrangian duality (2014)
  7. Yuan, Gonglin; Wei, Zengxin; Li, Guoyin: A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs (2014)
  8. Bagirov, A.M.; Jin, L.; Karmitsa, N.; Al Nuaimat, A.; Sultanova, N.: Subgradient method for nonconvex nonsmooth optimization (2013)
  9. Deb, Kalyanmoy; Gupta, Shivam; Dutta, Joydeep; Ranjan, Bhoomija: Solving dual problems using a coevolutionary optimization algorithm (2013)
  10. Mäkelä, Marko M.; Karmitsa, Napsu; Bagirov, Adil: Subgradient and bundle methods for nonsmooth optimization (2013)
  11. Sagastizábal, Claudia: Composite proximal bundle method (2013)
  12. Karmitsa, N.; Bagirov, A.; Mäkelä, M.M.: Comparing different nonsmooth minimization methods and software (2012)
  13. Bagirov, A.M.; Ugon, J.: Codifferential method for minimizing nonsmooth DC functions (2011)
  14. Karmitsa, Napsu; Mäkelä, Marko M.: Limited memory bundle method for large bound constrained nonsmooth optimization: convergence analysis (2010)
  15. Karmitsa, N.; Mäkelä, M.M.: Adaptive limited memory bundle method for bound constrained large-scale nonsmooth optimization (2010)
  16. Karmitsa, N.M.S.; Mäkelä, M.M.; Ali, M.M.: Limited memory interior point bundle method for large inequality constrained nonsmooth minimization (2008)
  17. Haarala, Napsu; Miettinen, Kaisa; Mäkelä, Marko M.: Globally convergent limited memory bundle method for large-scale nonsmooth optimization (2007)
  18. Bagirov, Adil M.; Ugon, Julien: Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization (2006)
  19. Miettinen, Kaisa; Mäkelä, Marko M.; Maaranen, Heikki: Efficient hybrid methods for global continuous optimization based on simulated annealing (2006)
  20. Haarala, M.; Miettinen, K.; Mäkelä, M.M.: New limited memory bundle method for large-scale nonsmooth optimization (2004)

Further publications can be found at: http://napsu.karmitsa.fi/publications/