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Contingent Derivatives of Implicit (Multi-) Functions and Stationary Points.
- Source :
- Annals of Operations Research; 2001, Vol. 101 Issue 1-4, p313-331, 19p
- Publication Year :
- 2001
-
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<subscript>x</subscript><superscript>-1</superscript> F<subscript>p</subscript> in the standard implicit function theorem for smooth F and Φ. This will be applied to the projection X(p) = {x ¦ 3y: (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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02545330
- Volume :
- 101
- Issue :
- 1-4
- Database :
- Complementary Index
- Journal :
- Annals of Operations Research
- Publication Type :
- Academic Journal
- Accession number :
- 18654725
- Full Text :
- https://doi.org/10.1023/A:1010957515360