Optimality Conditions

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


In this chapter we discuss first and second order optimality conditions for the optimization problem
, 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.


Lagrange Multiplier Feasible Point Constraint Qualification Exact Penalty Function Critical Cone 
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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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