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On Nonsmooth Optimality Conditions with Generalized Convexities

Marko M. Mäkelä, Ville-Pekka Eronen, Napsu Karmitsa, On Nonsmooth Optimality Conditions with Generalized Convexities. TUCS Technical Reports 1056, TUCS, 2012.

Abstract:

Optimality conditions are an essential part of mathematical optimization theory, affecting heavily, for example to the optimization method development. Different types of generalized
convexities have proved to be the main tool when constructing optimality conditions, particularly sufficient conditions for
optimality. The purpose of this paper is to present some sufficient and necessary optimality conditions for locally Lipschitz continuous multiobjective problems. In order to prove sufficient optimality conditions some generalized convexity properties for functions are introduced. For necessary optimality conditions we will need some constraint qualifications.

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BibTeX entry:

@TECHREPORT{tMxErKa12a,
  title = {On Nonsmooth Optimality Conditions with Generalized Convexities},
  author = {Mäkelä, Marko M. and Eronen, Ville-Pekka and Karmitsa, Napsu},
  number = {1056},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2012},
  keywords = {Generalized convexities; Clarke derivatives; nonsmooth analysis; nondifferentiable programming; optimality conditions; constraint qualifications},
}

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

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