Results 11 to 20 of about 1,032 (207)
On the theory of subdifferentials
Advances in Nonlinear Analysis, 2012 The theory presented in the paper consists of two parts. The first is devoted to basic concepts and principles such as the very concept of a subdifferential, trustworthiness and its characterizations, geometric consistence, fuzzy principles and calculus ...
Ioffe Alexander D.
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Subdifferential Calculus Using ϵ-Subdifferentials
Journal of Functional Analysis, 1993 AbstractIn applications of convex analysis it is important to be able to calculate the subdifferentials of various combinations of (proper and lower semicontinuous) convex functions, such as the sum of two such functions, or their inf-convolution ("epi-sum"), as well as the pre-composition of a convex function with an affine map or the "marginal ...
Hiriarturruty, J.B., Phelps, R.R.
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Symplectic Bregman Divergences [PDF]
EntropyWe present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality ...
Frank Nielsen
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A Duality Framework for Mathematical Programs with Tangential Subdifferentials
AlgorithmsThe aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials.
Vandana Singh +2 more
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Enlarged Inclusion of Subdifferentials
Canadian Mathematical Bulletin, 2005 AbstractThis paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f included in the γ-enlargement of the subdifferential of g, then the difference of those functions is γ-Lipschitz over their effective domain.
Thibault, Lionel, Zagrodny, Dariusz
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Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces [PDF]
Journal of Function Spaces, 2016 In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces.
Messaoud Bounkhel
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Vector subdifferentials and tangent cones [PDF]
Journal of Numerical Analysis and Approximation Theory, 2005 Following the Rockafellar's definition for the subdifferential of a real map we define a vector subdifferential using the normal cone to the epigraph of the function.
Cristina Stamate
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The properties of the weak subdifferentials
, 2010 This paper deals with the weak subdifferentials. The properties of the weak subdifferentials are examined. It is showed that the weak subdifferential of a function having a global minimum is not empty.
KASIMBEYLI, Refail, İNCEOĞLU, Gonca
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Dense subdifferentiability and trustworthiness for arbitrary subdifferentials
, 2010 We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions.
Jules, Florence, Lassonde, Marc
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Kuwait Journal of Science, 2021 In this work, interval-valued optimization problems are considered. Ordering cone is used in order to obtain a generalization of interval-valued optimization problems on real topological vector spaces.
Emrah KARAMAN
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