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Robust and continuous metric subregularity for linear inequality systems
This paper introduces two new variational properties, robust and continuous metric subregularity, for finite linear inequality systems under data...
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Generic linear convergence through metric subregularity in a variable-metric extension of the proximal point algorithm
The proximal point algorithm finds a zero of a maximal monotone map** by iterations in which the map** is made strongly monotone by the addition...
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Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions
This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as...
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Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity
With the help of bounded metric subregularity which is weaker than strong convexity, we show the linear convergence of proximal stochastic...
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Radius theorems for subregularity in infinite dimensions
The paper continues our previous work (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) on the radius of subregularity that was initiated by...
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A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity
We describe and analyze a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth map** over a polyhedral set. Such...
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Sufficient Conditions for Metric Subregularity of Constraint Systems with Applications to Disjunctive and Ortho-Disjunctive Programs
This paper is devoted to the study of the metric subregularity constraint qualification for general optimization problems, with the emphasis on the...
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Pseudo metric subregularity and its stability in Asplund spaces
As a variant of metric subregularity, pseudo metric subregularity is studied via general limit critical sets using the techniques of variational...
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On the Strong Subregularity of the Optimality Map** in an Optimal Control Problem with Pointwise Inequality Control Constraints
This paper presents sufficient conditions for strong metric subregularity (SMsR) of the optimality map** associated with the local Pontryagin...
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Strong Subregularity
“One-point” variants of the property of metric regularity can be obtained if in the definition we fix one of the points x or y at the reference...
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The Radius of Metric Regularity Revisited
The paper extends the radius of metric regularity theorem by Dontchev, Lewis and Rockafellar (2003) by providing an exact formula for the radius with...
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The Radius of Metric Subregularity
There is a basic paradigm, called here the radius of well-posedness , which quantifies the “distance” from a given well-posed problem to the set of...
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Directional Metric Pseudo Subregularity of Set-valued Map**s: a General Model
This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in...
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Sequential Constant Rank Constraint Qualifications for Nonlinear Semidefinite Programming with Algorithmic Applications
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from...
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\(\alpha \)-Firmly nonexpansive operators on metric spaces
We extend to p -uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate...
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Quadratic Growth and Linear Convergence of a DCA Method for Quartic Minimization over the Sphere
The quartic minimization over the sphere can be reformulated as a nonlinear nonconvex semidefinite program over the spectraplex. In this paper, under...
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New Set-Valued Directional Derivatives: Calculus and Optimality Conditions
In this paper, we propose a new notion called radial directional derivative and derive its existence as well as main calculus rules. Then we employ...
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Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity
We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for...
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Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems
We study linear convergence of some first-order methods such as the proximal gradient method (PGM), the proximal alternating linearized minimization...