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321
Lipschitz functions with minimal Clarke subdifferential mappings
, 1996
"... In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdifferential mapping of a realvalued locally Lipschitz function is a minimal weak cusco. We then use this characterisation to deduce some new results concerning Lipschitz functions with minimal subdifferenti ..."
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Cited by 3 (3 self)
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In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdifferential mapping of a realvalued locally Lipschitz function is a minimal weak cusco. We then use this characterisation to deduce some new results concerning Lipschitz functions with minimal
Separable determination of integrability and minimality of the Clarke subdifferential mapping
, 1997
"... In this paper we show that the study of integrability and Drepresentability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces. ..."
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Cited by 7 (1 self)
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In this paper we show that the study of integrability and Drepresentability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.
A comparison of bayesian methods for haplotype reconstruction from population genotype data.
 Am J Hum Genet
, 2003
"... In this report, we compare and contrast three previously published Bayesian methods for inferring haplotypes from genotype data in a population sample. We review the methods, emphasizing the differences between them in terms of both the models ("priors") they use and the computational str ..."
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Cited by 557 (7 self)
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, which combinations of alleles are present on each of the two chromosomes). Knowledge of the haplotypes carried by sampled individuals would be helpful in many settings, including linkagedisequilibrium mapping and inference of population evolutionary history, essentially because genetic inheritance
Generalized subdifferentials: a Baire categorical approach
, 1999
"... . We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that "almost every continuous realvalued funct ..."
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Cited by 7 (3 self)
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: Almost every 1Lipschitz function defined on a Banach space has a Clarke subdifferential mapping that is identically equal to the dual ball; If fT 1 ; T 2 ; : : : ; T n g is a family of maximal cyclically monotone operators defined on a Banach space X then there exists a realvalued locally Lipschitz
The Clarke and MichelPenot subdifferentials of the eigenvalues of a symmetric matrix
 Comput. Optim. Appl
, 1999
"... Abstract. We calculate the Clarke and MichelPenot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via the gener ..."
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Cited by 5 (0 self)
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Abstract. We calculate the Clarke and MichelPenot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via
T.: On the maximal monotonicity of subdifferential mappings
 Pacific Journal of Mathematics
, 1970
"... The subdifferential of a lower semicontinuous proper convex function on a Banach space is a maximal monotone operator, as well as a maximal cyclically monotone operator. This result was announced by the author in a previous paper, but the argument given there was incomplete; the result is proved her ..."
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Cited by 95 (0 self)
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The subdifferential of a lower semicontinuous proper convex function on a Banach space is a maximal monotone operator, as well as a maximal cyclically monotone operator. This result was announced by the author in a previous paper, but the argument given there was incomplete; the result is proved
Distinct Differentiable Functions May Share the Same Clarke Subdifferential at All Points
, 1995
"... . We construct, using Zahorski's Theorem, two everywhere differentiable realvalued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential. Keywords: Lipschitz function, differentiability, integrability, gene ..."
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Cited by 1 (0 self)
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, generalized derivative, Clarke subdifferential, approximate continuity, metric density. AMS (1991) subject classification: Primary 49J52; Secondary 26A27, 26A16. 1. Introduction. In recent years, four subdifferential maps have been widely used: the Clarke subdifferential, the MichelPenot subdifferential
Limiting Convex Examples for Nonconvex Subdifferential Calculus
, 1997
"... . We show, largely using convex examples, that most of the core results for limiting subdifferential calculus fail without additional restrictions in infinite dimensional Banach spaces. Key Words. Nonsmooth analysis, subdifferentials, coderivatives, extremal principle, open mapping theorem, metric r ..."
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Cited by 4 (2 self)
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. We show, largely using convex examples, that most of the core results for limiting subdifferential calculus fail without additional restrictions in infinite dimensional Banach spaces. Key Words. Nonsmooth analysis, subdifferentials, coderivatives, extremal principle, open mapping theorem, metric
Rotund Norms, Clarke Subdifferentials and Extensions of Lipschitz Functions
 Meth., Appl
, 1998
"... . We show that a certain condition regarding the separation of points by Lipschitz functions is useful in extending a given Lipschitz function from a subspace of a Banach space to the whole space so that the extension function has maximal Clarke subdierential. We then establish connections between t ..."
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Cited by 4 (1 self)
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. We show that a certain condition regarding the separation of points by Lipschitz functions is useful in extending a given Lipschitz function from a subspace of a Banach space to the whole space so that the extension function has maximal Clarke subdierential. We then establish connections between
THE CLARKE’S SUBDIFFERENTIAL FOR VECTOR VALUED FUNCTIONS
"... In this paper we examine the construction of Clarke's derivative for vectorvalued functions. We use another kind of Lipschitz functions, which allow us to leave the context of normed spaces. As base of the generalization we use the approach used by Clarke for real functions. For vectorvalued ..."
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valued functions, Clarke uses the Rademacher theorem, which is not available in general contexts. Keywords: directional derivative, subdifferential, vectorial functions AMS classification: 26A24, 46G05 1. Introductory notations and definitions Let F be an real ordered vector space, whose order relation is denoted
Results 1  10
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321