Regularity and Stability in Nonlinear Semi-Infinite Optimization

  • Diethard Klatte
  • René Henrion
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 25)


The paper is concerned with semi-infinite C 1 programs parametrized in the objective function and in the constraint functions, where perturbations may also occur in the index set of the semi-infinite constraints. Our purpose is to give a self-contained presentation of the interrelations between metric regularity, extended Mangasarian-Fromovitz constraint qualification, local boundedness of multipliers and upper semi-continuity of stationary solutions. Moreover, we outline stability properties of perturbed local minimizers in the absence of second-order differentiability of the data.


Constraint Qualification Cone Constraint Order Optimality Condition Local Boundedness Strict Local Minimizer 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Diethard Klatte
    • 1
  • René Henrion
    • 2
  1. 1.Institut für Operations ResearchUniversität ZürichZürichSwitzerland
  2. 2.Weierstraß-Institut für Angewandte Analysis und Stochastik, BerlinBerlinGermany

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