Results 11 to 20 of about 810 (214)
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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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
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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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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Integration of Fenchel subdifferentials revisited [PDF]
, 2014 We obtain a simple integration formula for the Fenchel subdifferentials on Euclidean spaces and analyze some of its consequences.
Martínez Legaz, Juan Enrique
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Abstract and Applied Analysis, 2002 In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations.
Noriaki Yamazaki
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Min–sup-type zero duality gap properties for DC composite optimization problem
Journal of Inequalities and Applications, 2019 In this paper, we present min–sup-type zero duality gap properties for DC composite optimization problem with conic constraints. Using properties of the subdifferentials of involved functions, we introduce some new constraint qualifications.
Li Ping Tian, Dong Hui Fang
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Integration of Fenchel subdifferentials revisited
, 2021 We obtain a simple integration formula for the Fenchel subdifferentials on Euclidean spaces and analyze some of its consequences.
Martínez Legaz, Juan Enrique
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Digital Chemical Engineering, 2023 With increasing digitalization and vertical integration of chemical process systems, nonconvex optimization problems often emerge in chemical engineering applications, yet require specialized optimization techniques.
Yingwei Yuan, Kamil A. Khan
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The Continuity of Subdifferential Mapping
Journal of Mathematical Analysis and Applications, 1997 The authors discuss continuity of the subdifferential mapping of the gauge of a bounded convex set with the origin an interior point and find a single-valuedness criterion for the mapping.
Wang, Jian-Hua, Nan, Chao-Xun
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