Results 111 to 120 of about 335 (149)
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On Metric and Calmness Qualification Conditions in Subdifferential Calculus
Set-Valued and Variational Analysis, 2008The authors derive criteria for calmness/subregularity in terms of outer subdifferentials and outer coderivatives for set-valued mappings between finite dimensional spaces. They discuss the relationship between the qualification conditions and establish the basic calculus rules of nonsmooth subdifferential calculus for sets, functions and set-valued ...
Alexander D Ioffe +2 more
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Nonlinear Analysis: Theory, Methods & Applications, 1995
The aim of this survey paper is to present calculus rules for the subdifferential \(\partial f\) of a convex function \(f\) constructed from other convex functions \(f_i\) by means of the main operations encountered in convex analysis, without any qualification conditions.
J -B Hiriart-Urruty, M Volle
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The aim of this survey paper is to present calculus rules for the subdifferential \(\partial f\) of a convex function \(f\) constructed from other convex functions \(f_i\) by means of the main operations encountered in convex analysis, without any qualification conditions.
J -B Hiriart-Urruty, M Volle
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Subdifferential Calculus Rules for Possibly Nonconvex Integral Functions
SIAM Journal on Control and Optimization, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafael Correa +2 more
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Journal of Global Optimization, 1994
The author provides an interesting survey about the calculus rules for the global approximate minimum \(\varepsilon\)-argmin\( f\) and the approximate subdifferential \(\partial_ \varepsilon f(x)\) (in the sense of convex analysis) of a not necessarily convex function \(f: X\to \mathbb{R}\).
M Volle, Volle M
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The author provides an interesting survey about the calculus rules for the global approximate minimum \(\varepsilon\)-argmin\( f\) and the approximate subdifferential \(\partial_ \varepsilon f(x)\) (in the sense of convex analysis) of a not necessarily convex function \(f: X\to \mathbb{R}\).
M Volle, Volle M
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Lebesgue infinite sums of convex functions: subdifferential calculus
, 2023 Summary: We present a subdifferential analysis for a general concept of infinite sum \(f:=\sum_{i\in I}f_{i}\) of arbitrary collections of convex functions \(f_{i}\), called Lebesgue infinite sum. Since this problem cannot be addressed, at least directly, through classical arguments from the theory of normal convex integrands, we perform a reduction ...
Hantoute, Abderrahim +2 more
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Sequential Convex Subdifferential Calculus and Sequential Lagrange Multipliers
SIAM Journal on Control and Optimization, 1997Summary: The aim of this paper is to establish formulas for the subdifferentials of the sum and the composition of convex functions in terms of the subdifferentials of the data functions at nearby points. Applications to general optimization problems lead to a new notion of sequential Lagrange multipliers.
Lionel Thibault
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Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces
Set-Valued and Variational Analysis, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nam, Nguyen Mau +2 more
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Nonconvex Separation Theorem for Multifunctions, Subdifferential Calculus and Applications
Set-Valued and Variational Analysis, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions [PDF]
SIAM Journal on Optimization, 2008 We provide a rule to calculate the subdifferential set of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space.
Abderrahim Hantoute +2 more
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Metric Inequality, Subdifferential Calculus and Applications
Set-Valued Analysis, 2001The aim of the paper is the presentation of calculus rules for the limiting Fréchet subdifferential of not necessarily Lipschitz functions on Asplund spaces and the application of these results to the derivation of necessary optimality conditions for nonsmooth constrained optimization problems.
Huynh Van Ngai, Théra, Michel
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