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Hölder metric subregularity with applications to proximal point method
 SIAM Journal on Optimization
, 2012
"... This paper is mainly devoted to the study and applications of Hölder metric subregularity (or metric qsubregularity of order q ∈ (0, 1]) for general setvalued mappings between infinitedimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we d ..."
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Cited by 7 (1 self)
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This paper is mainly devoted to the study and applications of Hölder metric subregularity (or metric qsubregularity of order q ∈ (0, 1]) for general setvalued mappings between infinitedimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and pointbased sufficient conditions as well as necessary conditions for qmetric subregularity with evaluating the exact subregularity bound, which are new even for the conventional (firstorder) metric subregularity in both finite and infinitedimensions. In this way we also obtain new fractional error bound results for composite polynomial systems with explicit calculating fractional exponents. Finally, metric qsubregularity is applied to conduct a quantitative convergence analysis of the classical proximal point method for finding zeros of maximal monotone operators on Hilbert spaces. 1
Metric Subregularity for proximal generalized equations in Hilbert Spaces
, 2011
"... In this paper, we introduce and consider the concept of the proxregularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or n ..."
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Cited by 3 (0 self)
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In this paper, we introduce and consider the concept of the proxregularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or necessary conditions for such a generalized equation to have the metric subregularity in Hilbert spaces. We also establish results of RobinsonUrsescu theorem type for proxregular multifunctions.
H.: About [q]regularity properties of collections of sets
 J. Math. Anal. Appl
, 1016
"... Abstract We examine three primal space local Hölder type regularity properties of finite collections of sets, namely, ..."
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Cited by 2 (1 self)
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Abstract We examine three primal space local Hölder type regularity properties of finite collections of sets, namely,
Algebraic Multigrid for Discrete Elliptic Second Order Problems. February 1996
, 1997
"... A Mixed Variational Formulation for 3D Magnetostatics and its Finite Element February 1996 ..."
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A Mixed Variational Formulation for 3D Magnetostatics and its Finite Element February 1996
CALCULUS OF TANGENT SETS AND DERIVATIVES OF SET VALUED MAPS UNDER METRIC SUBREGULARITY CONDITIONS
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