Optimality conditions for scalar and vector optimization problems with quasiconvex inequality constraints

Ginchev Ivan
Additional contact information
Ginchev Ivan: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: Let X be a real linear space, X0 -> X a convex set, Y and Z topological real linear spaces. The constrained optimization problem minCf(x), g(x) 2 -K is considered, where f : X0 ! Y and g : X0 ! Z are given (nonsmooth) functions, and C -> Y and K -> Z are closed convex cones. The weakly efficient solutions (w-minimizers) of this problem are investigated. When g obeys quasiconvex properties, first-order necessary and first-order sufficient optimality conditions in terms of Dini directional derivatives are obtained. In the special case of problems with pseudoconvex data it is shown that these conditions characterize the global w-minimizers and generalize known results from convex vector programming. The obtained results are applied to the special case of problems with finite dimensional image spaces and ordering cones the positive orthants, in particular to scalar problems with quasiconvex constraints. It is shown, that the quasiconvexity of the constraints allows to formulate the optimality conditions using the more simple single valued Dini derivatives instead of the set valued ones. Key words: Vector optimization, nonsmooth optimization, quasiconvex vector functions, pseudoconvex vector functions, Dini derivatives, quasiconvex programming, Kuhn-Tucker conditions..

Pages: 24 pages
Date: 2008-06
New Economics Papers: this item is included in nep-ind, nep-ipr, nep-pr~, nep-net and nep-ppm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.eco.uninsubria.it/RePEc/pdf/QF2008_5.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf0805

Access Statistics for this paper

More papers in Economics and Quantitative Methods from Department of Economics, University of Insubria Contact information at EDIRC.
Bibliographic data for series maintained by Segreteria Dipartimento ().