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Contingent Derivatives of Implicit (Multi-) Functions and Stationary Points

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  • Diethard Klatte
  • Bernd Kummer

Abstract

For an implicit multifunction Φ(p) defined by the generally nonsmooth equation F(x,p)=0, contingent derivative formulas are derived, being similar to the formula Φ′=−F x −1 F p in the standard implicit function theorem for smooth F and Φ. This will be applied to the projection X(p)={x∣∃y: (x,y)∈Φ(p)} of the solution set Φ(p) of the system F(x,y,p)=0 onto the x-space. In particular settings, X(p) may be interpreted as stationary solution sets. We discuss in detail the situation in which X(p) arises from the Karush–Kuhn–Tucker system of a nonlinear program. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Diethard Klatte & Bernd Kummer, 2001. "Contingent Derivatives of Implicit (Multi-) Functions and Stationary Points," Annals of Operations Research, Springer, vol. 101(1), pages 313-331, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:313-331:10.1023/a:1010957515360
    DOI: 10.1023/A:1010957515360
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