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Limited Memory Discrete Gradient Bundle Method for Nonsmooth Derivative Free Optimization

Napsu Karmitsa, Adil Bagirov, Limited Memory Discrete Gradient Bundle Method for Nonsmooth Derivative Free Optimization. TUCS Technical Reports 1011, Turku Centre for Computer Science, 2011.

Abstract:

Typically, practical optimization problems involve nonsmooth functions with hundreds of variables. Moreover, there are many practical problems where the computation of even one subgradient is either a difficult or an impossible task. In such cases derivative free methods are the better (or only) choice since they do not use explicit computation of subgradients. In this paper, we propose an efficient derivative free limited memory discrete gradient bundle method for nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions and the numerical experiments to be presented confirm the usability of the method especially for medium- and large-scale problems.

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BibTeX entry:

@TECHREPORT{tKaBa11a,
  title = {Limited Memory Discrete Gradient Bundle Method for Nonsmooth Derivative Free Optimization},
  author = {Karmitsa, Napsu and Bagirov, Adil},
  number = {1011},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2011},
  keywords = {Nondifferentiable optimization, derivative free   optimization, limited memory methods, bundle methods, discrete gradient.},
  ISBN = {978-952-12-2604-5},
}

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