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Stability and regular points of inequality systems
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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A fixed point theorem involving a hybrid inwardness‐contraction condition
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Ekeland, I. / Temam, R., Convex Analysis and Variational Problems. Amsterdam‐Oxford. North‐Holland Publ. Company. 1976. IX, 402 S., Dfl. 85.00. US $ 29.50 (SMAA 1)
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Czechoslovak Mathematical Journal
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Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming
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A remark on a regularity assumption for the mathematical programming problem in Banach spaces
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Perturbation theory for abstract optimization problems
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The lagrange multiplier set and the generalized gradient set of the marginal function of a differentiable program in a Banach space
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Regularity and stability for the mathematical programming problem in Banach spaces
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Refinements of necessary optimality conditions in nondifferentiable programming I
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Differential stability in infinite-dimensional nonlinear programming
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First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
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Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems
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Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
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Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming
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A unified theory of first and second order conditions for extremum problems in topological vector spaces
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On regularity conditions in mathematical programming
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Some examples and counterexamples for the stability analysis of nonlinear programming problems
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Principles of mathematical analysis
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On the variational principle
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A general theory of necessary optimality conditions
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Clarke's tangent cones and the boundaries of closed sets in Rn
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A characterization of tangential regularity
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Convex Analysis and Variational Problems
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An Algorithmic Approach to Nonlinear Analysis and Optimization
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Optimization by Vector Space Methods
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LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA
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Strong Derivatives and Inverse Mappings
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A Short Proof of the Variational Principle for Approximate Solutions of a Minimization Problem
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Necessary and sufficient conditions for quadratic minimality
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A Characterization of Complete Metric Spaces
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Completeness and the Contraction Principle
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Generalized Gradients and Applications
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Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
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Regular Points of Lipschitz Functions
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Nonsmooth analysis: differential calculus of nondifferentiable mappings
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Nonconvex minimization problems
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Directionally Lipschitzian Functions and Subdifferential Calculus
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Continuity and Differentiability Properties of Convex Operators
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An Algorithmic Approach to Nonlinear Analysis and Optimization
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Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space
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Implicit Functions and Optimization Problems without Continuous Differentiability of the Data
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Differential Stability in Nonlinear Programming
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Weak Tangent Cones and Optimization in a Banach Space
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Necessary and Sufficient Conditions for a Local Minimum. 1: A Reduction Theorem and First Order Conditions
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Nonsmooth Calculus in Finite Dimensions
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Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
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Conjugate Duality and Optimization
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1. Conjugate Duality and Optimization
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Optimization and Nonsmooth Analysis
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Regularity and Stability for Convex Multivalued Functions
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A New Approach to Lagrange Multipliers
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Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
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Multifunctions with convex closed graph
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On the inverse function theorem
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Generalized Directional Derivatives and Subgradients of Nonconvex Functions
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Directionally Lipschitzian Mappings on Baire Spaces
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Constraint Qualifications
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Subtraction Theorems and Approximate Openness for Multifunctions: Topological and Infinitesimal Viewpoints
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Inverse and Implicit Function Theorems for Nonsmooth Maps in Banach Spaces
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Solution Sensitivity of a Class of Variational Inequalities
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Convexity and Openness with Linear Rate
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Future Challenges for Variational Analysis
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Metric Regularity and Optimality Conditions in Nonsmooth Optimization
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Metric and Topological Tools
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Elements of Convex Analysis
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Elementary and Viscosity Subdifferentials
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Circa-Subdifferentials, Clarke Subdifferentials
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Limiting Subdifferentials
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Graded Subdifferentials, Ioffe Subdifferentials
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Regularity and Stability in Nonlinear Semi-Infinite Optimization
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Error Bounds for Quadratic Systems
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Prox-Regularity and Subjets
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Convex analysis and nonlinear optimization : theory and examples
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Set-Valued Analysis of Solution Mappings
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On the Merit and Penalty Functions for the D.C. Optimization
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Continuity for s-Convex Fuzzy Processes
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Convex Directional Derivatives in Optimization
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Tangent Cones and Tangent Sets
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Calculus for parabolic second-order derivatives
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On the convergence of von Neumann's alternating projection algorithm for two sets
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Metric regularity and subdifferential calculus in Banach spaces
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On regularity and stability in semi-infinite optimization
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Exact barrier function methods for Lipschitz programs
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Metric regularity of the feasible set mapping in semi-infinite optimization
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Metric regularity, tangent sets, and second-order optimality conditions
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Critical point theory for smooth functions on Hilbert manifolds with singularities and its application to some optimal control problems
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Approximate subdifferential and metric regularity: The finite-dimensional case
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Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
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Optimality conditions in mathematical programming and composite optimization
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A Gauss—Newton method for convex composite optimization
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Hölder behavior of optimal solutions and directional differentiability of marginal functions in nonlinear programming
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Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints
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Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point
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Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems
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Error bounds in mathematical programming
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Necessary Efficiency Conditions for Vector Equilibrium Problems with General Inequality Constraints via Convexificators
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Exact estimates of regularity modulus for infinite programming
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Nonlinear regularity models
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Convergence analysis of stationary points in sample average approximation of stochastic programs with second order stochastic dominance constraints
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On convergence of the Gauss-Newton method for convex composite optimization
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Metric regularity and quantitative stability in stochastic programs with probabilistic constraints
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Variational Methods in Convex Analysis
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Gauss–Newton method for convex composite optimizations on Riemannian manifolds
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On the Stability and Solution Sensitivity of a Consumer Problem
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Lipschitz-Like Property for Linear Constraint Systems
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Convex Difference Criteria for the Quantitative Stability of Parametric Quasidifferentiable Systems
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Pontryagin Maximum Principle for Control Systems on Infinite Dimensional Manifolds
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Metric Regularity of Quasidifferentiable Mappings and Optimality Conditions for Nonsmooth Mathematical Programming Problems
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Directional Metric Pseudo Subregularity of Set-valued Mappings: a General Model
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R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization
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S-convexity revisited (fuzzy): long version
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Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations
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Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps
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Second-order necessary conditions for optimality in nonsmooth nonlinear programming
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The drop theorem, the petal theorem and Ekeland's variational principle
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Metric regularity, openness and Lipschitzian behavior of multifunctions
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Differential characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions between Banach spaces
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Lipschitzian stability of constraint systems and generalized equations
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Metric regularity for strongly compactly Lipschitzian mappings
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Stable local minimizers in semi-infinite optimization: regularity and second-order conditions
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Global Lipschitzian error bounds for semidefinite complementarity problems with emphasis on NCPs
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Linear semi-openness and the Lyusternik theorem
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Normal coderivative for multifunctions and implicit function theorems
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Metric regularity and systems of generalized equations
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Strong metric subregularity of mappings in variational analysis and optimization
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Point-based sufficient conditions for metric regularity of implicit multifunctions
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Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions
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Tangent cone and contingent cone to the intersection of two closed sets
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Robinson metric regularity of parametric variational systems
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First and second order sufficient conditions for strict minimality in nonsmooth vector optimization
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Selected Bibliography of Works Not Cited
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Variational pairs and applications to stability in nonsmooth analysis
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Characterizations of strict local minima for some nonlinear programming problems
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Coderivatives of multivalued mappings, locally compact cones and metric regularity
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s-Convex fuzzy processes
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Locally compactly Lipschitzian mappings in infinite dimensional programming
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The approximate subdifferential of composite functions
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A chain rule for nonsmooth composite functions via minimisation
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On metric regularity of multifunctions
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On closed graph and implicit function theorems for multifunctions
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Characterization of Stability for Cone Increasing Constraint Mappings
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Scalarization of Tangential Regularity of Set-Valued Mappings
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Compactness Properties, Openness Criteria and Coderivatives
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Implicit Multifunction Theorems
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Subdifferential Evolution Inclusion in Nonconvex Analysis
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Upper Subderivatives and Generalized Gradients of the Marginal Function of a Non-Lipschitzian Program
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Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application
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Multivalued Analysis and Differential Properties of Multivalued Mappings
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An exact penalty method for D.C. optimization
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Regularity and strong sufficient optimality conditions in differentiable optimization problems
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Euler appoximation of the feasible set
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First order approximations to nonsmooth mappings with application to metric regularity
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On lagrange-kuhn-tucker multipliers for pareto optimization problems
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On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems
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A general metric regularity in asplund banach spaces
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Extensions of metric regularity
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A Mountain Pass Lemma and its implications regarding the uniqueness of constrained minimizers
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Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials
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On Lipschitz-like continuity of a class of set-valued mappings
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Isotone tangent cones and nonsmooth optimization
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Upper DSL Approximates and Nonsmooth Optimization
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A chain rule for parabolic second-order epiderivatives
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Sensitivity analysis for constraint and variational systems by means of set-valued differentiation
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Epiderivatives of the marginal function in nonsmooth parametric optimization
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Compactly epi-lipschitzian sets and a-subdifferentials in wt-spaces
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Second-order necessary optimality conditions via directional regularity
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Second order approximations and dual necessary optimality conditions
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Optimality conditions for mildly nonsmooth constrained optimization
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On the Bartle-Graves theorem
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Range inclusion for convex processes on Banach spaces; applications in controllability
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An Inverse Mapping Theorem for Set-Valued Maps
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Convex composite functions in Banach spaces and the primal lower-nice property
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Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization
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A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
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On Pseudo-Differentiability
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Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
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Verifiable Conditions for Openness and Regularity of Multivalued Mappings in Banach Spaces
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Nonsmooth Calculus in Finite Dimensions
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An Exact Penalization Viewpoint of Constrained Optimization
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Directional Regularity and Metric Regularity
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Majorizing Functions and Convergence of the Gauss–Newton Method for Convex Composite Optimization
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Classical Optimality Conditions under Weaker Assumptions
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Dini Derivatives of the Marginal Function of a Non-Lipschitzian Program
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An Induction Theorem and Nonlinear Regularity Models
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Coderivatives and the Solution Map of a Linear Constraint System
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Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints
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Robinson Stability of Parametric Constraint Systems via Variational Analysis
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Square-Root Metric Regularity and Related Stability Theorems for Smooth Mappings
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Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity
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Second-Order Conditions for Optimization Problems with Constraints
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Solution Stability of Nonsmooth Continuous Systems with Applications to Cone-Constrained Optimization
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Approximations and Metric Regularity in Mathematical Programming in Banach Space
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Implicit Functions, Lipschitz Maps, and Stability in Optimization
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On a Newton Type Iterative Method for Solving Inclusions
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Implicit functions defined by generalized equations
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Higher–Order Necessary Optimality Conditions for a Nonsmooth Extremum Problem
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Optimal control of differential inclusions on manifolds
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Stability analysis of parametric variational systems
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SENSITIVITY ANALYSIS FOR A CLASS OF IMPLICIT MULTIFUNCTIONS WITH APPLICATIONS
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Directionally Lipschitzian Mappings on Baire Spaces
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The Quantificational Tangent Cones
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Uniform Regularity of Set-Valued Mappings and Stability of Implicit Multifunctions
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Differentiability Properties of a Parametric Consumer Problem
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Stability of the optimal values under small perturbations of the constraint set
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Jonathan Michael Borwein 1951 − 2016: Life and Legacy
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Fixed Point Algorithms for Nonconvex Feasibility with Applications
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A Unified Theory for Metric Regularity of Multifunctions
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Variational Methods in Classical Open Mapping Theorems
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On weak sharp minima for a special class of nonsmooth functions
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