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Optimality Conditions

  • J. Frédéric Bonnans
  • Alexander Shapiro
Part of the Springer Series in Operations Research book series (ORFE)

Abstract

In this chapter we discuss first and second order optimality conditions for the optimization problem
(3.1)
, where f : X → IR, G : X → Y and Q and K are a nonempty closed convex subsets of X and Y, respectively. We can view the set Q as the domain of the objective function f. Unless stated otherwise, we assume that X and Y are Banach spaces and that f(x) and G(x) are continuous.

Keywords

Lagrange Multiplier Feasible Point Constraint Qualification Exact Penalty Function Critical Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • J. Frédéric Bonnans
    • 1
  • Alexander Shapiro
    • 2
  1. 1.INRIA-RocquencourtDomaine de VoluceauLe Chesnay CedexFrance
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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