The radius of metric regularity
From MaRDI portal
Publication:4779878
DOI10.1090/S0002-9947-02-03088-XzbMath1042.49026OpenAlexW1632219083MaRDI QIDQ4779878
Asen L. Dontchev, Adrian S. Lewis, R. Tyrrell Rockafellar
Publication date: 28 October 2002
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-02-03088-x
perturbationsmetric regularitycoderivativesRobinson-Ursescu theoremEckart-Young theoremdistance to infeasibilitydistance to irregularityLusternik-Graves theorem
Sensitivity, stability, well-posedness (49K40) Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)
Related Items
Pseudo metric subregularity and its stability in asplund spaces, Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations, Local linear convergence for alternating and averaged nonconvex projections, A proximal method for composite minimization, On the Bartle-Graves theorem, Stability of \(p\)-order metric regularity, Linear regularity, equirregularity, and intersection mappings for convex semi-infinite inequality systems, Exact estimates of regularity modulus for infinite programming, Towards variational analysis in metric spaces: metric regularity and fixed points, An Induction Theorem and Nonlinear Regularity Models, Uniformity and inexact version of a proximal method for metrically regular mappings, Directional Metric Regularity of Multifunctions, Stochastic Nash equilibrium problems: sample average approximation and applications, Implicit multifunction theorems in complete metric spaces, Metric regularity of epigraphical multivalued mappings and applications to vector optimization, Characterizations of stability of error bounds for convex inequality constraint systems, Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method, Bartle-Graves theorem revisited, On the inner and outer norms of sublinear mappings, Strong metric subregularity of mappings in variational analysis and optimization, Stability of metric regularity with set-valued perturbations and application to Newton's method for solving generalized equations, An improved stability result on the metric regularity under Lipschitz set-valued perturbations, Convexity of the images of small balls through nonconvex multifunctions, Lower semicontinuity of the feasible set mapping of linear systems relative to their domains, Some results on condition numbers in convex multiobjective optimization, Stability in linear optimization and related topics. A personal tour, The radius of metric subregularity, Robust and continuous metric subregularity for linear inequality systems, Radius theorems for subregularity in infinite dimensions, Regularity modulus of arbitrarily perturbed linear inequality systems, Convergence of the forward-backward algorithm: beyond the worst-case with the help of geometry, The radius of metric regularity revisited, A characterization of the distance to infeasibility under block-structured perturbations, Robinson metric regularity of parametric variational systems, Stability properties of the Tikhonov regularization for nonmonotone inclusions, Structure and stability of restrictively metrically regular mappings, Chain rules for linear openness in metric spaces and applications, METRIC REGULARITY—A SURVEY PART 1. THEORY, A metric version of Milyutin theorem, On metric regularity and the boundary of the feasible set in linear optimization, Implicit multifunction theorems with positively homogeneous maps, On mappings covering at a nonlinear rate and their perturbation stability, Metric subregularity for proximal generalized equations in Hilbert spaces, Pseudo-contractivity and metric regularity in fixed point theory, Lipschitz behavior of convex semi-infinite optimization problems: a variational approach, Regularity modulus and radius of set-valued mappings, Approximating stationary points of stochastic optimization problems in Banach space, About \([q\)-regularity properties of collections of sets], On regularity of convex multifunctions, Failure of metric regularity for major classes of variational systems, New Applications of Variational Analysis to Optimization and Control, Directional Hölder metric regularity, SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS, Perturbation Analysis of Metric Subregularity for Multifunctions, Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity, Regularity estimates for convex multifunctions, Metric regularity of the sum of multifunctions and applications, Metric subregularity for composite-convex generalized equations in Banach spaces, Metric regularity and systems of generalized equations, Metric subregularity for nonclosed convex multifunctions in normed spaces, Quantitative characterizations of regularity properties of collections of sets, On the block-structured distance to non-surjectivity of sublinear mappings, Conic systems and sublinear mappings: equivalent approaches., Uniform exponential convergence of sample average random functions under general sampling with applications in stochastic programming, Perturbations and metric regularity, Weak sharp efficiency and growth condition for vector-valued functions with applications, Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets, Convexity and Variational Analysis, Metric regularity of composition set-valued mappings: metric setting and coderivative conditions, Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems, Extensions of metric regularity†, Stability analysis of Gauss-type proximal point method for metrically regular mappings, Generalized Metric Subregularity and Regularity with Respect to an Admissible Function, On Some Open Problems in Optimal Control, Stability of Mann's iterates under metric regularity, The condition number of a function relative to a set, A Data-Independent Distance to Infeasibility for Linear Conic Systems, On the Lipschitz modulus of the argmin mapping in linear semi-infinite optimization, An inertial proximal scheme for nonmonotone mappings, Coderivative calculus and metric regularity for constraint and variational systems, On existence of solutions of parametrized generalized equations, Lyusternik-Graves theorem and fixed points, Smooth sample average approximation of stationary points in nonsmooth stochastic optimization and applications, Stability of indices in the KKT conditions and metric regularity in convex semi-infinite optimization, Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations, Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods, Iterative solving of variational inclusions under Wijsman perturbations, Tikhonov regularization of metrically regular inclusions, Approximation of Fixed Points of Metrically Regular Mappings, Metric subregularity and the proximal point method, Estimation of the modulus of Hölder metric regularity, Metric regularity of mappings and generalized normals to set images, Radius theorems for monotone mappings, Metric regularity of semi-infinite constraint systems, Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings, Slater Condition for Tangent Derivatives
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Metric regularity, tangent sets, and second-order optimality conditions
- Norm duality for convex processes and applications
- On condition numbers and the distance to the nearest ill-posed problem
- Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps
- Linear programming, complexity theory and elementary functional analysis
- Some characterizations and properties of the ``distance to the ill-posedness and the condition measure of a conic linear system
- Some mapping theorems
- Ill-Conditioned Convex Processes and Conic Linear Systems
- Matrix Analysis
- Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
- Regularity and Stability for Convex Multivalued Functions
- Strongly Regular Generalized Equations
- An Inverse Mapping Theorem for Set-Valued Maps
- Variational Analysis
- coderivatives of set-valued mappings: Calculus and applications
- On the Complexity of Solving Sparse Symmetric Linear Programs Specified with Approximate Data
- Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
- Understanding the Geometry of Infeasible Perturbations of a Conic Linear System
- Convex Analysis
- Normed Convex Processes
- Verification for existence of solutions of linear complementarity problems
- Ill-conditioned inclusions