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On constrained set-valued optimization

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  • Ginchev Ivan

    () (Department of Economics, University of Insubria, Italy)

  • Rocca Matteo

    () (Department of Economics, University of Insubria, Italy)

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    Abstract

    The set-valued optimization problem minC F(x), G(x)\(-K) 6= ; is considered, where F : Rn Rm and G : Rn Rp are set-valued functions, and C Rm and K Rp are closed convex cones. Two type of solutions, called w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers), are treated. In terms of the Dini set-valued directional derivative first-order necessary conditions for a point to be a w-minimizer, and first-order sufficient conditions for a point to be an i-minimizer are established, both in primal and dual form. Key words: Set-valued optimization, First-order optimality conditions, Dini derivatives.

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    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0710.

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    Length: 8 pages
    Date of creation: Oct 2007
    Date of revision:
    Handle: RePEc:ins:quaeco:qf0710

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