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New Multiple Subgradient Descent Bundle Method for Nonsmooth Multiobjective Optimization

Outi Wilppu, Napsu Karmitsa, Marko M. Mäkelä, New Multiple Subgradient Descent Bundle Method for Nonsmooth Multiobjective Optimization. TUCS Technical Reports 1126, TUCS, 2014.

Abstract:

The aim of this paper is to propose a new multiple subgradient descent bundle method for solving unconstrained convex nonsmooth multiobjective optimization problems. Contrary to many existing multiobjective optimization methods, our method treats the objective functions as they are without employing any scalarization. The main idea is to find descent directions for every objective function separately and then form a common descent direction for every objective function. In addition, we prove that the method is convergent and it finds weakly Pareto optimal solutions. Finally, some numerical experiments are considered.

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BibTeX entry:

@TECHREPORT{tWiKaMx14a,
  title = {New Multiple Subgradient Descent Bundle Method for Nonsmooth Multiobjective Optimization},
  author = {Wilppu, Outi and Karmitsa, Napsu and Mäkelä, Marko M.},
  number = {1126},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2014},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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