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

  • Ginchev Ivan

    ()

    (Department of Economics, University of Insubria, Italy)

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    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..

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    File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2008_5.pdf
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    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0805.

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    Length: 24 pages
    Date of creation: Jun 2008
    Date of revision:
    Handle: RePEc:ins:quaeco:qf0805
    Contact details of provider: Postal: Via Ravasi 2-21100 Varese
    Web page: http://www.uninsubria.it/uninsubria/facolta/econo.html

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    1. Josh Lerner & Jean Tirole, 2002. "The Scope of Open Source Licensing," NBER Working Papers 9363, National Bureau of Economic Research, Inc.
    2. Lerner, Josh & Tirole, Jean, 2002. "Some Simple Economics of Open," Journal of Industrial Economics, Wiley Blackwell, vol. 50(2), pages 197-234, June.
    3. Comino, Stefano & Manenti, Fabio M., 2011. "Dual licensing in open source software markets," Information Economics and Policy, Elsevier, vol. 23(3), pages 234-242.
    4. West, Joel, 2003. "How open is open enough?: Melding proprietary and open source platform strategies," Research Policy, Elsevier, vol. 32(7), pages 1259-1285, July.
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