Search Results - Convex functions and convex programs in convex geometry

Proximal decomposition of convex optimization via an alternating linearization algorithm with inexact oracles

Authors: Huang, Ming He, Yue Qiao, Ping-Ping et al.

Source: Journal of Industrial and Management Optimization. 20:3355-3372

Subject Terms: Convex programming, Numerical optimization and variational techniques, convex optimization, Convex functions and convex programs in convex geometry, Nonsmooth analysis, inexact oracles, nonsmooth optimization, alternating linearization method

File Description: application/xml

Access URL: https://zbmath.org/7901707
https://doi.org/10.3934/jimo.2024057

A convex function satisfying the Łojasiewicz inequality but failing the gradient conjecture both at zero and infinity

Authors: Daniilidis, Aris Haddou, Mounir Ley, Olivier et al.

Contributors: Daniilidis, Aris Haddou, Mounir Ley, Olivier et al.

Source: Bulletin of the London Mathematical Society. 54:590-608

Subject Terms: convex function, Geometric methods in ordinary differential equations, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Dynamical Systems (math.DS), 01 natural sciences, Real-analytic functions, Convex functions and convex programs in convex geometry, Optimization and Control (math.OC), FOS: Mathematics, convergence of secants, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Dynamical Systems, 0101 mathematics, gradient conjecture at infinity, Gradient conjecture, Mathematics - Optimization and Control, Kurdyka-Lojasiewicz inequality, Convexity of real functions of several variables, generalizations

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Access URL: http://arxiv.org/abs/2102.05342
https://zbmath.org/7729782
https://doi.org/10.1112/blms.12586
https://hal.science/hal-03136550v2
https://hal.science/hal-03136550v2/document
https://doi.org/10.1112/blms.12586

Sensitivity Analysis of Optimal Value Functions of Convex Parametric Programs with Possibly Empty Solution Sets: Sensitivity analysis of optimal value functions of convex parametric programs with possibly empty solution sets

Authors: Alberto Seeger Mohammed Moussaoui Seeger, Alberto

Contributors: Alberto Seeger Mohammed Moussaoui Seeger, Alberto

Source: SIAM Journal on Optimization. 4:659-675

Subject Terms: Convex programming, Convex functions and convex programs in convex geometry, sensitivity analysis, Sensitivity, stability, parametric optimization, 0211 other engineering and technologies, subdifferential, optimal value function, [MATH] Mathematics [math], 02 engineering and technology, convex program

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Access URL: https://hal.archives-ouvertes.fr/hal-02182375
https://epubs.siam.org/doi/abs/10.1137/0804038
https://doi.org/10.1137/0804038

On sums and convex combinations of projectors onto convex sets

Authors: Xianfu Wang Minh N. Bùi Heinz H. Bauschke

Source: Journal of Approximation Theory. 242:31-57

Subject Terms: Convex programming, convex set, 0211 other engineering and technologies, 47H05, 47H09, 47L07 (Primary), 46A32, 52A05, 52A41, 90C25 (Secondary), Convex sets without dimension restrictions (aspects of convex geometry), 02 engineering and technology, convex cone, 01 natural sciences, Functional Analysis (math.FA), Mathematics - Functional Analysis, convex combination, sum of projectors, Convex functions and convex programs in convex geometry, Optimization and Control (math.OC), monotone operator, partial sum property, proximity operator, FOS: Mathematics, Convex sets and cones of operators, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, Spaces of linear operators, topological tensor products, approximation properties, 0101 mathematics, projection operator, Monotone operators and generalizations, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/pdf/1802.02287
http://arxiv.org/abs/1802.02287
https://zbmath.org/7050069
https://doi.org/10.1016/j.jat.2019.02.001
https://www.sciencedirect.com/science/article/pii/S0021904519300176
https://api.elsevier.com/content/article/PII:S0021904519300176?httpAccept=text/xml
https://doi.org/10.1016/j.jat.2019.02.001
https://dblp.uni-trier.de/db/journals/jat/jat242.html#BauschkeBW19
http://ui.adsabs.harvard.edu/abs/2018arXiv180202287B/abstract

Rock Extensions with Linear Diameters: Rock extensions with linear diameters

Authors: Volker Kaibel Kirill Kukharenko

Source: SIAM Journal on Discrete Mathematics. 38:2982-3003

Subject Terms: polytope diameter, Convex functions and convex programs in convex geometry, Hirsch conjecture, Linear programming, extended formulation, linear programming, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)

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Access URL: https://zbmath.org/7959404
https://doi.org/10.1137/23m1585878

Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems: Convergence and recovery guarantees of unsupervised neural networks for inverse problems

Authors: Buskulic, Nathan Fadili, Jalal M. Quéau, Yvain et al.

Contributors: Buskulic, Nathan Fadili, Jalal M. Quéau, Yvain et al.

Source: Journal of Mathematical Imaging and Vision. 66:584-605

Subject Terms: Inverse problems, FOS: Computer and information sciences, Inverse problems for PDEs, Computer Science - Machine Learning, inverse problems, overparametrization, Nonsmooth analysis, 0211 other engineering and technologies, 02 engineering and technology, deep image/inverse prior, unsupervised learning, Unsupervised learning, 01 natural sciences, Deep Image/Inverse Prior, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Machine Learning (cs.LG), gradient flow, Convex functions and convex programs in convex geometry, Gradient flow, Overparametrization, 0101 mathematics, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2309.12128

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

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Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam: Extremal approximately convex functions and the best constants in a theorem of Hyers and Ulam.

Authors: James W. Roberts Ralph Howard Stephen J. Dilworth

Source: Advances in Mathematics. 172:1-14

Subject Terms: convex functions, approximately convex functions, Mathematics(all), best constants, Metric Geometry (math.MG), 26B25, 41A44, 01 natural sciences, Functional Analysis (math.FA), Mathematics - Functional Analysis, Convex functions and convex programs in convex geometry, Mathematics - Metric Geometry, FOS: Mathematics, Hyers-Ulam theorem, 0101 mathematics, Hyers–Ulam theorem, Convexity of real functions of several variables, generalizations

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Access URL: http://arxiv.org/abs/math/0011239
https://zbmath.org/1888326
https://doi.org/10.1006/aima.2001.2058
http://ui.adsabs.harvard.edu/abs/2000math.....11239D/abstract
https://core.ac.uk/display/82590901
https://www.sciencedirect.com/science/article/pii/S0001870801920584
https://dialnet.unirioja.es/servlet/articulo?codigo=320838
https://people.math.sc.edu/howard/Reprints/ulam-hyers-abstract.pdf

HESSIAN MEASURES OF CONVEX FUNCTIONS AND APPLICATIONS TO AREA MEASURES: Hessian measures of convex functions and applications to area measures

Authors: COLESANTI, ANDREA D. HUG

Source: Journal of the London Mathematical Society. 71:221-235

Subject Terms: Length, area, volume, other geometric measure theory, Abstract differentiation theory, differentiation of set functions, convex function, convex functions, \(j\)-extreme point, Convex functions and convex programs in convex geometry, Hausdorff and packing measures, Hessian measure, 0101 mathematics, Convex sets in \(n\) dimensions (including convex hypersurfaces), Radon-Nikodym derivative, 01 natural sciences

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Access URL: http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=280427
https://documat.unirioja.es/servlet/articulo?codigo=2206367
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610704005915
https://dialnet.unirioja.es/servlet/articulo?codigo=2206367
https://academic.oup.com/jlms/article/71/1/221/932659
https://www.uni-due.de/~hm0045/Pub.collection/33.pdf
https://hdl.handle.net/2158/251065

Maximal Monotone Operators, Convex Functions and a Special Family of Enlargements: Maximal monotone operators, convex functions and a special family of enlargements

Authors: Benar Fux Svaiter Regina S. Burachik

Source: Set-Valued Analysis. 10:297-316

Subject Terms: convex functions, Banach spaces, Convex functions and convex programs in convex geometry, Variational and other types of inequalities involving nonlinear operators (general), enlargements, 0211 other engineering and technologies, 02 engineering and technology, Maximal monotone operators, transportation formula, Monotone operators and generalizations

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Access URL: https://www.sid.ir/En/Journal/ViewPaper.aspx?ID=381990
https://link.springer.com/article/10.1023%2FA%3A1020639314056
https://rd.springer.com/article/10.1023/A%3A1020639314056
https://link.springer.com/content/pdf/10.1023/A:1020639314056.pdf

Every closed convex set is the set of minimizers of some $C^{\infty }$-smooth convex function: Every closed convex set is the set of minimizers of some \(C^{\infty}\)-smooth convex function

Authors: Juan Ferrera Daniel Azagra

Source: Proceedings of the American Mathematical Society. 130:3687-3692

Subject Terms: Normed linear spaces and Banach spaces, Banach lattices, Convex functions and convex programs in convex geometry, Derivatives of functions in infinite-dimensional spaces, Mosco limit, Hausdorff limit, Existence theories for problems in abstract spaces, smooth approximation of convex sets, 0101 mathematics, 01 natural sciences, closed convex sets

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Access URL: https://www.ams.org/proc/2002-130-12/S0002-9939-02-06695-9/S0002-9939-02-06695-9.pdf
https://www.jstor.org/stable/info/1194411
https://www.ams.org/journals/proc/2002-130-12/S0002-9939-02-06695-9/home.html
https://dialnet.unirioja.es/servlet/articulo?codigo=682943
https://www.ams.org/proc/2002-130-12/S0002-9939-02-06695-9/S0002-9939-02-06695-9.pdf

Well-positioned Closed Convex Sets and Well-positioned Closed Convex Functions: Well-positioned closed convex sets and well-positioned closed convex functions

Authors: Adly, Samir Ernst, Emil Théra, Michel et al.

Contributors: Adly, Samir Ernst, Emil Théra, Michel et al.

Source: Journal of Global Optimization. 29:337-351

Subject Terms: barrier cone, convex analysis, 0211 other engineering and technologies, Stability, separation, extension, and related topics for functional equations, [MATH] Mathematics [math], 02 engineering and technology, variational inequality, 01 natural sciences, support function, recession analysis, support functional, Convex functions and convex programs in convex geometry, semi-coercive functional, Fenchel conjugate, [MATH]Mathematics [math], semi-coercive functions, 0101 mathematics, Monotone operators and generalizations

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Access URL: https://hal.archives-ouvertes.fr/hal-00068258/file/AETW.pdf
https://hal.science/hal-00068258v1/document
https://hal.science/hal-00068258v1
https://doi.org/10.1023/b:jogo.0000047907.66385.5d
https://hal.archives-ouvertes.fr/hal-00068258/document
https://doi.org/10.1023/B:JOGO.0000047907.66385.5d
https://hal.archives-ouvertes.fr/hal-00068258
https://link.springer.com/article/10.1023/B:JOGO.0000047907.66385.5d

Lipschitz sums of convex functions

Authors: Assaf Naor Marianna Csörnyei

Source: Studia Mathematica. 158:269-286

Subject Terms: convex functions, Lipschitz functions, Convex functions and convex programs in convex geometry, convex sets, \(\Delta\)--convex functions, Convex sets without dimension restrictions (aspects of convex geometry), 0101 mathematics, 01 natural sciences, Convexity of real functions of several variables, generalizations

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/90152?download.pdf
https://nyuscholars.nyu.edu/en/publications/lipschitz-sums-of-convex-functions
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-3-6
https://collaborate.princeton.edu/en/publications/lipschitz-sums-of-convex-functions
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/158/3/90152/lipschitz-sums-of-convex-functions
https://www.impan.pl/shop/publication/transaction/download/product/90152?download.pdf

Some Analytical Properties of γ-Convex Functions in Normed Linear Spaces: Some analytical properties of \(\gamma\)-convex functions in normed linear spaces

Authors: Hoang Xuan Phu N. N. Hai

Source: Journal of Optimization Theory and Applications. 126:685-700

Subject Terms: Generalized convexity, generalized monotonicity, 0209 industrial biotechnology, Convex functions and convex programs in convex geometry, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, 0211 other engineering and technologies, \(\gamma\)-convex functions, 02 engineering and technology, rough convexity, boundedness, Nonconvex programming, global optimization, continuity

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Access URL: https://ideas.repec.org/a/spr/joptap/v126y2005i3d10.1007_s10957-005-5503-7.html
https://link.springer.com/article/10.1007/s10957-005-5503-7

An O(n) invariant rank 1 convex function that is not polyconvex: An \(O(n)\) invariant rank 1 convex function that is not polyconvex

Authors: M. Silhavy

Source: Theoretical and Applied Mechanics, Vol 2002, Iss 28-29, Pp 325-336 (2002)

Subject Terms: Convex functions and convex programs in convex geometry, rank \(1\) convexity, Methods involving semicontinuity and convergence, relaxation, polyconvexity, Mechanics of engineering. Applied mechanics, Nonlinear elasticity, Energy minimization in equilibrium problems in solid mechanics, TA349-359, 0101 mathematics, 01 natural sciences, Convexity of real functions of several variables, generalizations

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Access URL: http://www.doiserbia.nb.rs/ft.aspx?id=1450-55840229325S
https://zbmath.org/2124493
https://doaj.org/article/3e958b25538e44dca9c36093dd212f8e
http://www.doiserbia.nb.rs/img/doi/1450-5584/2002/1450-55840229325S.pdf
http://www.doiserbia.nb.rs/Article.aspx?ID=1450-55840229325S

Convex Functions and Their Applications : A Contemporary Approach

Authors: Constantin P. Niculescu Lars-Erik Persson

Resource Type: eBook.

Subjects: Functional analysis, Convex functions, Functions of real variables, Discrete geometry, Convex geometry

Categories: MATHEMATICS / Mathematical Analysis, MATHEMATICS / Discrete Mathematics, MATHEMATICS / Geometry / Analytic, MATHEMATICS / Functional Analysis

On strongly convex sets and strongly convex functions

Authors: E. S. Polovinkin

Source: Journal of Mathematical Sciences. 100:2633-2681

Subject Terms: Axiomatic and generalized convexity, Methods involving semicontinuity and convergence, relaxation, generating set, Minkowski-Pontryagin difference, \(M\)-strongly convex hull, 02 engineering and technology, Convex sets in \(n\) dimensions (including convex hypersurfaces), 01 natural sciences, Convex functions and convex programs in convex geometry, generating function, \(R\)-strongly extreme point, 0202 electrical engineering, electronic engineering, information engineering, Selections in general topology, \(m\)-strongly convex function, 0101 mathematics, Homotopy and topological questions for infinite-dimensional manifolds, \(M\)-strongly convex set, Convexity of real functions of several variables, generalizations

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Access URL: https://link.springer.com/article/10.1007/BF02672709

Φ-Convex Functions Defined on Metric Spaces: \(\Phi\)-convex functions defined on metric spaces

Authors: S. Rolewicz

Source: Journal of Mathematical Sciences. 115:2631-2652

Subject Terms: Programming in abstract spaces, Nonsmooth analysis, 0211 other engineering and technologies, subdifferential, 02 engineering and technology, Fréchet and Gateaux differentiability in optimization, 01 natural sciences, Banach spaces, Convex functions and convex programs in convex geometry, Fréchet differentiability, 0101 mathematics, Set-valued and variational analysis, Convexity of real functions of several variables, generalizations, Asplund theorem

File Description: application/xml

Access URL: https://zbmath.org/1982008
https://doi.org/10.1023/a:1023296417861
https://rd.springer.com/article/10.1023/a:1023296417861
https://link.springer.com/article/10.1023%2FA%3A1023296417861

Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers

Authors: Levent Tunçel Van Anh Truong

Source: Mathematical Programming. 100:295-316

Subject Terms: Convex programming, Numerical mathematical programming methods, Convex functions and convex programs in convex geometry, Numerical methods based on nonlinear programming, Linear programming, 0211 other engineering and technologies, homogeneous convex cones, Interior-point methods, 02 engineering and technology, self-concordant barriers, duality mapping

File Description: application/xml

Access URL: https://zbmath.org/2106481
https://doi.org/10.1007/s10107-003-0470-y

The Vector Partition Problem for Convex Objective Functions: The vector partition problem for convex objective functions.

Authors: Shmuel Onn Leonard J. Schulman

Source: Mathematics of Operations Research. 26:583-590

Subject Terms: Convex programming, Combinatorial optimization, Convex functions and convex programs in convex geometry, Partitions of sets, Analysis of algorithms and problem complexity, 0211 other engineering and technologies, 02 engineering and technology, Partition, cluster, optimization, separation, convex, polytope, zonotope, signing, vertex enumeration, polynomial time, combinatorial optimization

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Access URL: https://zbmath.org/1677177
https://doi.org/10.1287/moor.26.3.583.10587
https://pubsonline.informs.org/doi/abs/10.1287/moor.26.3.583.10587
https://dblp.uni-trier.de/db/journals/mor/mor26.html#OnnS01
http://ie.technion.ac.il/~onn/Selected/MOR2.pdf
https://ideas.repec.org/a/inm/ormoor/v26y2001i3p583-590.html
https://core.ac.uk/display/22602106
https://doi.org/10.1287/moor.26.3.583.10587