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

Diethard Klatte () and Bernd Kummer ()

Annals of Operations Research, 2001, vol. 101, issue 1, 313-331

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

Keywords: contingent derivative; implicit multifunction; derivative formulas; stationary solution; Karush–Kuhn–Tucker system (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1010957515360

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