Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms
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Publication:3426238
DOI10.1080/02331930600819787zbMath1113.49028OpenAlexW2009214374MaRDI QIDQ3426238
Publication date: 8 March 2007
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/02331930600819787
Ekeland's principleLipschitz stabilitygeneralized equationKojima function(nonsmooth) Newton methodmodified successive approximation
Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)
Related Items
Newton's method for generalized equations: a sequential implicit function theorem ⋮ Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland's principle ⋮ On the Newton method for set-valued maps ⋮ Optimization methods and stability of inclusions in Banach spaces ⋮ Error bounds: necessary and sufficient conditions ⋮ Error bounds and metric subregularity
Cites Work
- Unnamed Item
- Metric regularity, tangent sets, and second-order optimality conditions
- Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
- Subdifferentials of compactly Lipschitzian vector-valued functions
- An implicit-function theorem for \(C^{0,1}\)-equations and parametric \(C^{1,1}\)-optimization
- Sensitivity analysis for nonsmooth generalized equations
- Generalized Kojima-functions and Lipschitz stability of critical points
- On NCP-functions
- Lipschitzian inverse functions, directional derivatives, and applications in \(C^{1,1}\) optimization
- Proto-derivative formulas for basic subgradient mappings in mathematical programming
- A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems
- Solution of monotone complementarity problems with locally Lipschitzian functions
- On the variational principle
- Regularity and conditioning of solution mappings in variational analysis
- Some mapping theorems
- Solution Sensitivity from General Principles
- Isolated zeros of lipschitzian metrically regular -Functions
- Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem
- Strict (ε, δ)-Subdifferentials and Extremality Conditions
- Stability in Mathematical Programming with Nondifferentiable Data
- Calmness and Exact Penalization
- Generalized equations: Solvability and regularity
- The Local Convergence of Broyden-Like Methods on Lipschitzian Problems in Hilbert Spaces
- Exact Penalties for Local Minima
- Strongly Regular Generalized Equations
- On generalized differentials and subdifferentials of Lipschitz vector-valued functions
- Generalized equations and their solutions, part II: Applications to nonlinear programming
- Semismooth and Semiconvex Functions in Constrained Optimization
- Generalized equations and their solutions, Part I: Basic theory
- Mixed Coderivatives of Set–Valued Mappings in Variational Analysis
- Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
- Stability Theory for Parametric Generalized Equations and Variational Inequalities Via Nonsmooth Analysis
- Variational Analysis
- Metric regularity and subdifferential calculus
- Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
- Constrained Minima and Lipschitzian Penalties in Metric Spaces
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Variational conditions and the proto-differentiation of partial subgradient mappings
- Prox-regular functions in variational analysis
- Stability of Locally Optimal Solutions
- Metric regularity: characterizations, nonsmooth variations and successive approximation∗
- Strong Lipschitz Stability of Stationary Solutions for Nonlinear Programs and Variational Inequalities
- A subdifferential condition for calmness of multifunctions
