Implicit function theorems for generalized equations
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Publication:1904661
DOI10.1007/BF01585930zbMath0843.49010MaRDI QIDQ1904661
Publication date: 7 January 1996
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
sensitivityvariational inequalityimplicit function theoremsgeneralized equationsdirectional differentiability
Sensitivity, stability, well-posedness (49K40) Variational inequalities (49J40) Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Implicit function theorems, Jacobians, transformations with several variables (26B10)
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Cites Work
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- Well-posed optimization problems
- Sensitivity analysis for nonsmooth generalized equations
- On concepts of directional differentiability
- Newton's Method for B-Differentiable Equations
- Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
- Strongly Regular Generalized Equations
- An Implicit-Function Theorem for a Class of Nonsmooth Functions
- Strong Derivatives and Inverse Mappings
- Sensitivity Analysis of Parametrized Programs via Generalized Equations
- Existence and Differentiability of Metric Projections in Hilbert Spaces
- An Inverse Mapping Theorem for Set-Valued Maps
- Implicit Functions, Lipschitz Maps, and Stability in Optimization
- Sensitivity Analysis of Solutions to Generalized Equations
- A Note on Inverse Function Theorems