First-Order Conditions for C0,1 Constrained Vector Optimization

  • I. Ginchev
  • A. Guerraggio
  • M. Rocca
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


For a Fritz John type vector optimization problem with C 0,1 data we give scalar characterizations of its solutions applying the so called oriented distance and give necessary and sufficient first order optimality conditions in terms of the Dini derivative. While establishing the sufficiency, we introduce new type of efficient points referred to as isolated minimizers of first order. We show that the obtained necessary conditions are necessary for weak efficiency, and the sufficient conditions are sufficient and under Kuhn-Tucker type constraint qualification also necessary for a point to be an isolated minimizer of first order.

Key words

Vector optimization Nonsmooth optimization C0,1 functions Dini derivatives First-order optimality conditions Lagrange multipliers 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • I. Ginchev
    • 1
  • A. Guerraggio
    • 2
  • M. Rocca
    • 2
  1. 1.Department of MathematicsTechnical University of VarnaVarnaBulgaria
  2. 2.Department of EconomicsUniversity of InsubriaVareseItaly

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