Tangentially ds functions

Authors: CAPRARI, ELISA, Penot Jean Paul

Contributors: Caprari, Elisa, Penot Jean, Paul

Source: Optimization. 56:25-38

Subject Terms: NONSMOOTH ANALYSIS, GENERALIZED CONVEXITY, 0211 other engineering and technologies, CALCULUS OF FUNCTIONS ON INFINITE-DIMENSIONAL SPACES, 02 engineering and technology

File Description: STAMPA

Access URL: http://lma.univ-pau.fr/data/pub/pub_pdf2005/0528.pdf
http://www.tandfonline.com/doi/abs/10.1080/02331930600816023

Hölder continuous homomorphisms between infinite-dimensional Lie groups are smooth

Authors: Helge Glöckner

Source: Journal of Functional Analysis. 228:419-444

Subject Terms: Calculus of functions on infinite-dimensional spaces, Differentiability, Infinite-dimensional Lie group, Group Theory (math.GR), 01 natural sciences, Continuous and differentiable maps in nonlinear functional analysis, 22E65 (Primary) 26E15, 26E20, 26E30, 46T20, 58C20 (Secondary), Power map, FOS: Mathematics, 0101 mathematics, Calculus of functions taking values in infinite-dimensional spaces, Hölder continuity, Taylor expansion, Infinite-dimensional Lie groups and their Lie algebras: general properties, Lipschitz continuity, Smoothness, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analysis on \(p\)-adic Lie groups, Homomorphism, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions, non-Archimedean functional analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, Mathematics - Group Theory, infinite-dimensional Lie group, Analysis, differentiability

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0403251
https://www.sciencedirect.com/science/article/pii/S0022123605002892
https://core.ac.uk/display/82696344

An Approximate Rolle’s Theorem for Polynomials of Degree Four in a Hilbert Space: An approximate Rolle's theorem for polynomials of degree four in a Hilbert space

Authors: Jesús Ferrer

Source: Publications of the Research Institute for Mathematical Sciences. 41:375-384

Subject Terms: Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, (Spaces of) multilinear mappings, polynomials, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=41&iss=2&rank=7
https://zbmath.org/2230584
https://doi.org/10.2977/prims/1145475359
http://www.kurims.kyoto-u.ac.jp/~prims/pdf/41-2/41-2-16.pdf
https://www.kurims.kyoto-u.ac.jp/~prims/pdf/41-2/41-2-16.pdf
https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=41&iss=2&rank=7
http://ci.nii.ac.jp/naid/110001240007

Conveniently Hölder Homomorphisms are Smooth in the Convenient Sense: Conveniently Hölder homomorphisms are smooth in the convenient sense

Authors: Helge Glöckner

Source: Annals of Global Analysis and Geometry. 27:227-255

Subject Terms: Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, Group Theory (math.GR), 01 natural sciences, Hölder condition, Continuous and differentiable maps in nonlinear functional analysis, Lie group, 22E65 (Primary) 26E15, 26E20, 46T20, 58C20 (Secondary), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, convenient differential calculus, FOS: Mathematics, 0101 mathematics, Mathematics - Group Theory

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0404344v1.pdf
http://arxiv.org/abs/math/0404344
https://link.springer.com/article/10.1007/s10455-005-0040-z

Prox-regular functions in Hilbert spaces

Authors: Frédéric Bernard, Lionel Thibault

Source: Journal of Mathematical Analysis and Applications. 303:1-14

Subject Terms: Calculus of functions on infinite-dimensional spaces, proximal mapping, Derivatives of functions in infinite-dimensional spaces, prox-regular function, Applied Mathematics, Nonsmooth analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, subdifferential, primal lower nice function, 0101 mathematics, 01 natural sciences, Analysis, Moreau envelope

File Description: application/xml

Access URL: https://zbmath.org/2141737
https://doi.org/10.1016/j.jmaa.2004.06.003
https://www.sciencedirect.com/science/article/abs/pii/S0022247X04004718
http://ui.adsabs.harvard.edu/abs/2005JMAA..303....1B/abstract
https://core.ac.uk/display/82003022
https://www.sciencedirect.com/science/article/pii/S0022247X04004718

Uniform prox-regularity of functions and epigraphs in Hilbert spaces

Authors: F. Bernard, Lionel Thibault

Source: Nonlinear Analysis. 60:187-207

Subject Terms: Calculus of functions on infinite-dimensional spaces, prox-regular sets, uniformly prox-regular functions, epigraph, Nonsmooth analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Set-valued and function-space-valued mappings on manifolds, prox-regular functions, 0101 mathematics, Nonconvex programming, global optimization, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0362546X04002834

Bump Functions with Hölder Derivatives: Bump functions with Hölder derivatives

Authors: Thierry Gaspari

Source: Canadian Journal of Mathematics. 56:699-715

Subject Terms: range of derivatives, Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, Continuity and differentiation questions, 0101 mathematics, 01 natural sciences, Continuous and differentiable maps in nonlinear functional analysis, smooth bump functions

File Description: application/xml

Access URL: https://dialnet.unirioja.es/servlet/articulo?codigo=983154

Linearization of class C1 for contractions on Banach spaces: Linearization of class \(C^{1}\) for contractions on Banach spaces

Authors: Hildebrando M. Rodrigues, J. Solà-Morales

Source: Journal of Differential Equations. 201:351-382

Subject Terms: Normal forms for dynamical systems, Calculus of functions on infinite-dimensional spaces, Equations involving nonlinear operators (general), Dynamical systems involving smooth mappings and diffeomorphisms, Linearization, Conjugacy, 0101 mathematics, General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations, Fixed-point theorems on manifolds, Damped wave equation, 01 natural sciences, Analysis, Continuous and differentiable maps in nonlinear functional analysis

File Description: application/xml

Access URL: https://upcommons.upc.edu/bitstream/2117/2824/1/0301sola.pdf
http://www.sciencedirect.com/science/article/pii/S0022039604000737
https://upcommons.upc.edu/bitstream/handle/2117/2824/0301sola.pdf;sequence=1
https://www.sciencedirect.com/science/article/abs/pii/S0022039604000737
https://upcommons.upc.edu/handle/2117/2824
http://ui.adsabs.harvard.edu/abs/2004JDE...201..351R/abstract

Differential calculus over general base fields and rings: Differential calculus over general base fields and rings.

Authors: Karl-Hermann Neeb, Wolfgang Bertram, Helge Glöckner

Source: Expositiones Mathematicae. 22:213-282

Subject Terms: non-archimedian analysis, Mathematics(all), Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, infinite-dimensional Lie groups, topological fields, polynomial maps, rational manifolds, 01 natural sciences, non-archimedean analysis, differential calculus, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, 0101 mathematics, infinite-dimensional manifolds

File Description: application/xml

Access URL: https://zbmath.org/2222515
https://doi.org/10.1016/s0723-0869(04)80006-9
https://www.sciencedirect.com/science/article/abs/pii/S0723086904800069
http://tubiblio.ulb.tu-darmstadt.de/8352/
https://hal.archives-ouvertes.fr/hal-00141431
https://www.sciencedirect.com/science/article/pii/S0723086904800069

A Strong Optimization Theorem in Locally Convex Spaces: A strong optimization theorem in locally convex spaces

Authors: Cheng, L. X., Teng, Y. M.

Source: Chinese Annals of Mathematics. 24:395-402

Subject Terms: convex function, Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, locally convex space, geometry of infinite dimensions, 15. Life on land, convexification of nonconvex function, 01 natural sciences, 12. Responsible consumption, Geometry and structure of normed linear spaces, 11. Sustainability, 8. Economic growth, 0101 mathematics, optimization, differentiability

File Description: application/xml

Integral Newton-Type Polynomials with Continual Nodes: Integral Newton-type polynomials with continual nodes

Authors: Volodymyr L. Makarov, V. V. Khlobystov, B. R. Mikhal'chuk, E. F. Kashpur

Source: Ukrainian Mathematical Journal. 55:942-955

Subject Terms: Calculus of functions on infinite-dimensional spaces, interpolant, operator polynomial, (Spaces of) multilinear mappings, polynomials, continual integral, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/B%3AUKMA.0000010594.60504.08

New Sequential Lagrange Multiplier Conditions Characterizing Optimality without Constraint Qualification for Convex Programs: New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs

Authors: Nguyen Nang Dinh, Vaithilingam Jeyakumar, Gue Myung Lee

Source: SIAM Journal on Optimization. 14:534-547

Subject Terms: Convex programming, Calculus of functions on infinite-dimensional spaces, sequential \(\epsilon\)-subgradient optimality conditions, Convex functions and convex programs in convex geometry, 0211 other engineering and technologies, necessary and sufficient conditions, 02 engineering and technology, \(\varepsilon\)-subdifferential

File Description: application/xml

Extensions of generalized differential calculus in Asplund spaces

Authors: Bingwu Wang, Boris S. Mordukhovich

Source: Journal of Mathematical Analysis and Applications. 272:164-186

Subject Terms: Calculus of functions on infinite-dimensional spaces, generalized differential calculus, Asplund spaces, Applied Mathematics, Nonsmooth analysis, coderivatives, set-valued mappings, 0101 mathematics, subdifferentials, 01 natural sciences, normal cones, Analysis, Set-valued and variational analysis

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0022247X0200149X
https://www.sciencedirect.com/science/article/pii/S0022247X0200149X

Metric Inequality, Subdifferential Calculus and Applications: Metric inequality, subdifferential calculus and applications

Authors: Michel Théra, Huynh Van Ngai

Source: Set-Valued Analysis. 9:187-216

Subject Terms: Calculus of functions on infinite-dimensional spaces, Asplund spaces, Nonsmooth analysis, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, necessary optimality conditions, lower-semicontinuous functions, metric inequality, nonsmooth constrained optimization, Nonlinear programming, chain rule, 0101 mathematics, limiting Fréchet subdifferential

File Description: application/xml

Access URL: https://zbmath.org/1656464
https://doi.org/10.1023/a:1011291608129
https://www.unilim.fr/laco/rapports/2000/R2000_13.pdf
https://link.springer.com/article/10.1023/A%3A1011291608129

Subdifferential Regularity of Directionally Lipschitzian Functions: Subdifferential regularity of directionally Lipschitzian functions

Authors: L. Thibault, M. Bounkhel

Source: Canadian Mathematical Bulletin. 43:25-36

Subject Terms: Hadamard subdifferential, Calculus of functions on infinite-dimensional spaces, Clarke subdifferentials, directionally Lipschitz functions, subdifferential regularity, Nonsmooth analysis, 0211 other engineering and technologies, Hadamard directional derivative, 02 engineering and technology, 16. Peace & justice, Fréchet and Gateaux differentiability in optimization, 01 natural sciences, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, directional regularity, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/1462901
https://doi.org/10.4153/cmb-2000-004-5
https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/subdifferential-regularity-of-directionally-lipschitzian-functions/41A76533FDCADC27E67EDF20EDDBD25E
https://cms.math.ca/cmb/abstract/pdf/149139.pdf

Fuzzy Principles and Characterization of Trustworthiness: Fuzzy principles and characterization of trustworthiness

Authors: Alexander D. Ioffe

Source: Set-Valued Analysis. 6:265-276

Subject Terms: extremal principle, Calculus of functions on infinite-dimensional spaces, Nonsmooth analysis, 0211 other engineering and technologies, lower semicontinuous functions, subdifferential calculus, 02 engineering and technology, 0101 mathematics, local basic fuzzy principles, trustworthiness, 01 natural sciences, nonlocal basic fuzzy principle, multi-directional mean-value inequality

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A:1008614315547

The Equivalence of Several Basic Theorems for Subdifferentials: The equivalence of several basic theorems for subdifferentials

Authors: Qiji J. Zhu

Source: Set-Valued Analysis. 6:171-185

Subject Terms: Calculus of functions on infinite-dimensional spaces, sum rules, \(\beta\)-subdifferentials, Asplund spaces, Nonsmooth analysis, 0211 other engineering and technologies, \(\beta\)-subgradient, 02 engineering and technology, 0101 mathematics, Fréchet subdifferentiability, 01 natural sciences, extremal principles

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A%3A1008656207314

Sequential Convex Subdifferential Calculus and Sequential Lagrange Multipliers: Sequential convex subdifferential calculus and sequential Lagrange multipliers

Authors: Lionel Thibault

Source: SIAM Journal on Control and Optimization. 35:1434-1444

Subject Terms: Programming in abstract spaces, Convex programming, Calculus of functions on infinite-dimensional spaces, Convex functions and convex programs in convex geometry, sequential Lagrange multipliers, Nonsmooth analysis, 0211 other engineering and technologies, 02 engineering and technology, sequential subdifferential calculus, subdifferentials, \(\varepsilon\)-subdifferential

File Description: application/xml

Access URL: https://epubs.siam.org/doi/10.1137/S0363012995287714
https://locus.siam.org/doi/abs/10.1137/S0363012995287714

Convexity Criteria for Set-Valued Maps: Convexity criteria for set-valued maps

Authors: Nguyen Dong Yen, Pham Huu Sach

Source: Set-Valued Analysis. 5:37-45

Subject Terms: set-valued maps, convex functions, Calculus of functions on infinite-dimensional spaces, contingent derivative, 0101 mathematics, Set-valued functions, Set-valued operators, 01 natural sciences, Convexity of real functions of several variables, generalizations, Set-valued maps in general topology

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A%3A1008657617548

Some remarks on Rademacher's theorem in infinite dimensions

Authors: Vladimir I. Bogachev, E. Mayer-Wolf

Source: Potential Analysis. 5:23-30

Subject Terms: Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, Lipschitz property, linear space provided with a bounded Radon measure, Wiener space, infinite-dimensional version of Rademacher's theorem, Measures and integration on abstract linear spaces, Stochastic analysis, 0101 mathematics, 01 natural sciences, differentiability

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF00276694