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.)

File Description: application/xml

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

Contributors: Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Normandie Université (NU), École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), ANR-19-CHIA-0017,DEEP-VISION,DEEP-VISION(2019)

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

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

Authors: Huang, Ming, He, Yue, Qiao, Ping-Ping, Lin, Si-Da, Li, Dan, Yang, Yang

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

Contributors: Ley, Olivier, Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile Santiago (UCHILE), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

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

File Description: application/xml; application/pdf

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

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

File Description: application/xml

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

Discrete Convexity: Discrete convexity

Authors: Danilov, V. I., Koshevoj, G. A.

Source: Journal of Mathematical Sciences. 133:1418-1421

Subject Terms: polymatroidal discretely concave functions, Convex functions and convex programs in convex geometry, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), separation theorem, Convexity of real functions of several variables, generalizations

File Description: application/xml

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

File Description: application/xml

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

Convex risk measures for portfolio optimization and concepts of flexibility

Authors: Lüthi, Hans-Jakob, Doege, Jörg

Source: Mathematical Programming, 104 (2-3)

Subject Terms: Convex programming, Portfolio theory, Convex functions and convex programs in convex geometry, Risk theory, insurance, Sensitivity, stability, parametric optimization, 0502 economics and business, 05 social sciences, 0211 other engineering and technologies, 02 engineering and technology

File Description: application/xml; application/application/pdf

Access URL: https://www.research-collection.ethz.ch/bitstream/20.500.11850/31176/2/10107_2005_Article_628.pdf
https://zbmath.org/2238693
https://doi.org/10.1007/s10107-005-0628-x
http://hdl.handle.net/20.500.11850/31176
http://doc.rero.ch/record/318271/files/10107_2005_Article_628.pdf

Some problems about the representation of monotone operators by convex functions

Authors: Jean-Paul Penot, Constantin Zălinescu

Source: The ANZIAM Journal. 47:1-20

Subject Terms: convex function, Convex functions and convex programs in convex geometry, multifunction, 0211 other engineering and technologies, subdifferential, 02 engineering and technology, Monotone operators and generalizations, maximal monotone operator

File Description: application/xml

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F6BF4DABB104B3ABDA09278DBA23905A/S1446181100009731a.pdf/div-class-title-some-problems-about-the-representation-of-monotone-operators-by-convex-functions-div.pdf
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F6BF4DABB104B3ABDA09278DBA23905A/S1446181100009731a.pdf/div-class-title-some-problems-about-the-representation-of-monotone-operators-by-convex-functions-div.pdf
https://www.cambridge.org/core/journals/anziam-journal/article/some-problems-about-the-representation-of-monotone-operators-by-convex-functions/F6BF4DABB104B3ABDA09278DBA23905A
https://documat.unirioja.es/servlet/articulo?codigo=1265871
https://dialnet.unirioja.es/servlet/articulo?codigo=1265871

Slice-continuous sets in reflexive Banach spaces: convex constrained optimization and strict convex separation

Authors: Constantin Zălinescu, Emil Ernst, Michel Théra

Source: Journal of Functional Analysis. 223:179-203

Subject Terms: Slice-continuous set, Well-positioned set, Asymptote, Convex programming, strict convex separation, slice-continuous set, Stability, separation, extension, and related topics for functional equations, Continuous set, well-positioned set, 01 natural sciences, constrained optimization, Strict convex separation, Convex functions and convex programs in convex geometry, asymptote, continuous set, Existence theories for problems in abstract spaces, 0101 mathematics, Constrained optimization, Monotone operators and generalizations, Analysis

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Access URL: https://www.sciencedirect.com/science/article/pii/S0022123604003118
https://core.ac.uk/display/82347040

Integration of ε-Fenchel Subdifferentials and Maximal Cyclic Monotonicity: Integration of \(\epsilon\)-Fenchel subdifferentials and maximal cyclic monotonicity

Authors: Lionel Thibault, Sylvie Marcellin

Source: Journal of Global Optimization. 32:83-91

Subject Terms: convex functions, cyclically monotone families of operators, Convex functions and convex programs in convex geometry, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, Nonsmooth analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, \(\epsilon\)-Fenchel subdifferentials, 0211 other engineering and technologies, 02 engineering and technology, 0101 mathematics, integration of \(\epsilon\)-Fenchel subdifferentials, 01 natural sciences, Convexity of real functions of several variables, generalizations

File Description: application/xml

Access URL: https://zbmath.org/2215001
https://doi.org/10.1007/s10898-004-5905-3
https://link.springer.com/article/10.1007%2Fs10898-004-5905-3
https://link.springer.com/content/pdf/10.1007/s10898-004-5905-3.pdf

Mathematics of Plott choice functions

Authors: Vladimir I. Danilov, Gleb A. Koshevoy

Source: Mathematical Social Sciences. 49:245-272

Subject Terms: Inverse image, Choice function, 05 social sciences, Lattice, Social choice, 0102 computer and information sciences, Linear order, Direct image, 01 natural sciences, Convex structure, Path independence, Convex geometry, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Convex functions and convex programs in convex geometry, Circuit, 0502 economics and business, FOS: Mathematics, Simple word, Mathematics - Combinatorics, Combinatorics (math.CO), Varieties of lattices

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0304171
http://arxiv.org/abs/math/0304171
https://econpapers.repec.org/article/eeematsoc/v_3a49_3ay_3a2005_3ai_3a3_3ap_3a245-272.htm
http://mathecon.cemi.rssi.ru/danilov/files/article-Plott.pdf
https://www.sciencedirect.com/science/article/pii/S0165489604000770
http://dblp.uni-trier.de/db/journals/mss/mss49.html#DanilovK05
https://ideas.repec.org/a/eee/matsoc/v49y2005i3p245-272.html

Ultramodular Functions: Ultramodular functions.

Authors: MARINACCI, Massimo, MONTRUCCHIO, Luigi

Source: Mathematics of Operations Research. 30:311-332

Subject Terms: Axiomatic and generalized convexity, Convex functions and convex programs in convex geometry, Cooperative games, supermodularity, convexity, essentially smooth functions, cooperative games, convex ordering, 0101 mathematics, Nonconvex programming, global optimization, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2228388
https://doi.org/10.1287/moor.1040.0143
http://dl.acm.org/citation.cfm?id=1067203.1067244
http://www.biblioecon.unito.it/biblioservizi/RePEc/icr/wp2003/Marinacci-Montrucchio13-03.pdf
https://hdl.handle.net/2318/1196

New Generalized Convexity Notion for Set-Valued Maps and Application to Vector Optimization: New generalized convexity notion for set-valued maps and application to vector optimization

Authors: P. H. Sach

Source: Journal of Optimization Theory and Applications. 125:157-179

Subject Terms: generalized convexity, set-valued maps, Convex functions and convex programs in convex geometry, efficiency, 0211 other engineering and technologies, 02 engineering and technology, 0101 mathematics, Nonconvex programming, global optimization, 01 natural sciences, Multi-objective and goal programming, alternative theorems, Set-valued and variational analysis, Benson proper efficiency

File Description: application/xml

Access URL: https://zbmath.org/2174507
https://doi.org/10.1007/s10957-004-1716-4
https://link.springer.com/content/pdf/10.1007/s10957-004-1716-4.pdf
https://link.springer.com/article/10.1007/s10957-004-1716-4

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

File Description: application/xml

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

Remarks on the Analytic Centers of Convex Sets: Remarks on the analytic centers of convex sets

Authors: Wiesława T. Obuchowska

Source: Computational Optimization and Applications. 29:69-90

Subject Terms: Convex programming, analytic centre, Convex functions and convex programs in convex geometry, interior point methods, 0211 other engineering and technologies, perturbed convex programs, Interior-point methods, 02 engineering and technology, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2128734
https://doi.org/10.1023/b:coap.0000039489.72939.35
https://dblp.uni-trier.de/db/journals/coap/coap29.html#Obuchowska04
https://doi.org/10.1023/B:COAP.0000039489.72939.35
https://link.springer.com/article/10.1023%2FB%3ACOAP.0000039489.72939.35

The relevance of convex analysis for the study of monotonicity

Authors: Jean-Paul Penot

Source: Nonlinear Analysis. 58:855-871

Subject Terms: sum of operators, 0211 other engineering and technologies, 02 engineering and technology, Fenchel conjugation, Set-valued functions, maximal monotone operator, 01 natural sciences, Convex functions and convex programs in convex geometry, composition, monotone operator, 0101 mathematics, Monotone operators and generalizations, Convex sets in topological vector spaces (aspects of convex geometry), Set-valued operators

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0362546X04002123

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

Contributors: Vieceli, Yolande, Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation (LACO), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596 (LMMT), Université Paul Cézanne - Aix-Marseille 3, MOD

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

File Description: application/pdf; application/xml

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

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

Existence of solutions for nonlinear inequalities in locally convex separated space

Authors: Rabia Nessah

Source: Bulletin des Sciences Mathématiques. 128:417-431

Subject Terms: Noncooperative games, Mathematics(all), g-saddle point, Convex functions and convex programs in convex geometry, Variational and other types of inequalities involving nonlinear operators (general), Games with infinitely many players, abstract nonlinear inequality, Inequalities and extremum problems involving convexity in convex geometry, Abstract nonlinear inequality, Variational inequalities (global problems) in infinite-dimensional spaces, 0101 mathematics, Aumann strong equilibrium, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0007449704000387
https://core.ac.uk/display/82030903
https://www.sciencedirect.com/science/article/pii/S0007449704000387