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Multiobjective Proximal Bundle Method for Nonsmooth Optimization

Marko M. Mäkelä, Napsu Karmitsa, Outi Wilppu, Multiobjective Proximal Bundle Method for Nonsmooth Optimization. TUCS Technical Reports 1120, TUCS, 2014.

Abstract:

We present a proximal bundle method for finding weakly Pareto optimal
solutions to constrained nonsmooth programming problems with
multiple objectives. The method is a generalization of proximal bundle approach
for single objective optimization.
The multiple objective functions are treated individually without
employing any scalarization. The method is globally convergent and
capable of handling several nonconvex locally Lipschitz continuous
objective functions subject to nonlinear (possibly nondifferentiable)
constraints. Under some generalized convexity assumptions, we prove that the method finds
globally weakly Pareto optimal solutions. Concluding, some numerical examples illustrate the properties and
applicability of the method. In addition, we give a collection of multiobjective test problems.

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BibTeX entry:

@TECHREPORT{tMxKaWi14a,
  title = {Multiobjective Proximal Bundle Method for Nonsmooth Optimization},
  author = {Mäkelä, Marko M. and Karmitsa, Napsu and Wilppu, Outi},
  number = {1120},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2014},
}

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

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