Search Results - approximate coderivative*

Approximate subgradients and coderivatives in R n: Approximate subgradients and coderivatives in \(R^ n\)

Authors: Borwein, D. Borwein, J. M. Wang, Xianfu

Source: Set-Valued Analysis. 4:375-398

Subject Terms: coderivative, Mordukhovich-Ioffe coderivatives, Lipschitz function, Lebesgue measure, subgradients, Nonsmooth analysis, nowhere dense set, subgradient, Convex sets in \(n\) dimensions (including convex hypersurfaces), Fréchet and Gateaux differentiability in optimization, 01 natural sciences, bump function, disconnectedness, Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives, generalized Jacobian, vector-valued Lipschitz functions, gauge, guage, Calculus of vector functions, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/980809
https://doi.org/10.1007/bf00436112
https://link.springer.com/article/10.1007%2FBF00436112
http://docserver.carma.newcastle.edu.au/152/

Chain Rules for Coderivatives of Multivalued Mappings in Banach Spaces

Authors: Jourani, A. Thibault, L.

Source: Proceedings of the American Mathematical Society, 1998 May 01. 126(5), 1479-1485.

Access URL: https://www.jstor.org/stable/118803

Qualification Conditions for Calculus Rules of Coderivatives of Multivalued Mappings: Qualification conditions for calculus rules of coderivatives of multivalued mappings

Authors: Abderrahim Jourani L Thibault

Source: Journal of Mathematical Analysis and Applications. 218:66-81

Subject Terms: Derivatives of functions in infinite-dimensional spaces, multivalued mappings with closed graphs, coderivatives of multivalued mappings, Applied Mathematics, Nonsmooth analysis, limiting Fréchet coderivatives, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, Asplund space, approximate coderivative, calculus rules, tangent cones, 0101 mathematics, Set-valued operators, Analysis

File Description: application/xml

Access URL: https://zbmath.org/1123511
https://doi.org/10.1006/jmaa.1997.5733
https://www.sciencedirect.com/science/article/pii/S0022247X97957334
https://core.ac.uk/display/81126860
https://www.sciencedirect.com/science/article/abs/pii/S0022247X97957334

Approximate Subgradients and Coderivatives in R n

Authors: J.M. Borwein J. M. Borwein Xianfu Wang et al.

Contributors: J.M. Borwein J. M. Borwein Xianfu Wang et al.

Source: http://www.cecm.sfu.ca/ftp/pub/CECM/Preprints/Postscript/96:058-Borwein-Borwein-Wang.ps.gz.

Subject Terms: Subgradient, coderivative, generalized Jacobian, Lipschitz function, bump function, gauge, nowhere dense set, Lebesgue measure, disconnectedness

File Description: application/postscript

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.5220

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.5220
http://www.cecm.sfu.ca/ftp/pub/CECM/Preprints/Postscript/96:058-Borwein-Borwein-Wang.ps.gz

Chain rules for coderivatives of multivalued mappings in Banach spaces

Authors: Abderrahim Jourani Lionel Thibault

Source: Proceedings of the American Mathematical Society. 126:1479-1485

Subject Terms: coderivative, nonsmooth analysis, multivalued mapping, Nonsmooth analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, chain rule, 0101 mathematics, 01 natural sciences, approximate subdifferential

File Description: application/xml

Access URL: https://www.ams.org/proc/1998-126-05/S0002-9939-98-04198-7/S0002-9939-98-04198-7.pdf
https://zbmath.org/1132410
https://doi.org/10.1090/s0002-9939-98-04198-7
https://www.ams.org/journals/proc/1998-126-05/S0002-9939-98-04198-7/home.html
https://www.ams.org/proc/1998-126-05/S0002-9939-98-04198-7/S0002-9939-98-04198-7.pdf

Variational analysis of paraconvex multifunctions

Authors: Van Ngai, Huynh Tron, Nguyen Van Vu, Nguyen et al.

Subject Terms: 4901 Applied mathematics, Approximate convex function, Coderivatives, Fréchet normal cone, Fréchet subdifferential, Fuzzy mean value theorem, Lower C2 functions, Paraconvexity, Paramonotonicity, Weak convexity

Relation: Journal of Optimization Theory and Applications Vol. 193, no. 1-3 (2022), p. 180-218; https://purl.org/au-research/grants/arc/DP160100854; http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185174; vital:16646

Availability: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185174
https://doi.org/10.1007/s10957-022-02021-2

Approximate subgradients and coderivatives in R n

Authors: Borwein, D. Borwein, J. M. Wang, Xianfu

Subject Terms: subgradient, coderivative, generalized Jacobian, Lipschitz function, bump function, guage, nowhere dense set, Lebesgue measure, disconnectedness

Relation: Set-Valued Analysis Vol. 4, Issue 4, p. 375-398; http://hdl.handle.net/1959.13/940911; uon:13131

Availability: http://hdl.handle.net/1959.13/940911

Exact Penalization and Optimality Conditions for Approximate Directional Minima

Authors: Chelmus, Teodor

Source: Taiwanese Journal of Mathematics, 2022 Feb 01. 26(1), 201-219.

Access URL: https://www.jstor.org/stable/27117793

Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces.

Authors: Mordukhovich, Boris S. Wu, Pengcheng Yang, Xiaoqi

Source: Optimization; Sep2025, Vol. 74 Issue 11, p2577-2610, 34p

Subject Terms: STABILITY criterion, BANACH spaces, LIPSCHITZ continuity, CALCULUS of variations, SET-valued maps, VARIATIONAL approach (Mathematics), MATHEMATICAL optimization

OPTIMAL CONTROL OF IMPLICIT POLYHEDRAL SWEEPING PROCESSES INVOLVING THE CODERIVATIVE OF THE PROJECTION MAPPING.

Authors: ALSHARIEF, LAILA JOURANI, ABDERRAHIM

Source: SIAM Journal on Control & Optimization; 2025, Vol. 63 Issue 4, p2856-2886, 31p

Subject Terms: OPTIMAL control theory, METRIC projections, VARIATIONAL inequalities (Mathematics), SUBDIFFERENTIALS, LOTKA-Volterra equations, DIFFERENTIAL inclusions, POLYHEDRA

Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces.

Authors: Zheng, Xi Li, Runxin

Source: Journal of Optimization Theory & Applications. Aug2014, Vol. 162 Issue 2, p665-679. 15p.

Subject Terms: *HILBERT space, *LAGRANGE multiplier, *MATHEMATICAL optimization, *PARETO analysis, *VECTOR analysis, *FUZZY sets

Lagrange multiplier rules for weak approximate Pareto solutions to constrained vector optimization problems with variable ordering structures.

Authors: Hu, Chunhai Zhu, Jiangxing

Source: Optimization. Jul2022, Vol. 71 Issue 7, p2131-2155. 25p.

Subject Terms: *CONSTRAINED optimization, *LAGRANGE multiplier, *SUBDIFFERENTIALS, *CONES

Optimisation of parabolic type polyhedral discrete, discrete-approximate and differential inclusions.

Authors: Mahmudov, Elimhan N. Mastaliyeva, Dilara

Source: International Journal of Control; Sep2024, Vol. 97 Issue 9, p2073-2083, 11p

Subject Terms: DIFFERENTIAL inclusions, SET-valued maps

Approximate Convexity for Set-Valued Maps.

Authors: Kefayati, Zohreh Oveisiha, Morteza

Source: Mathematics Interdisciplinary Research; Dec2023, Vol. 8 Issue 4, p337-345, 9p

Subject Terms: SET-valued maps, APPROXIMATION theory, SUBDIFFERENTIALS, MONOTONIC functions, CONVEX functions

Approximate solutions for robust multiobjective optimization programming in Asplund spaces.

Authors: Saadati, Maryam Oveisiha, Morteza

Source: Optimization; Feb2024, Vol. 73 Issue 2, p329-357, 29p

Subject Terms: NONSMOOTH optimization, ROBUST optimization, CONVEX functions

Exact Penalization and Optimality Conditions for Approximate Directional Minima

Authors: Teodor Chelmuş

Source: Taiwanese Journal of Mathematics. 26

Subject Terms: 0211 other engineering and technologies, 02 engineering and technology

Access URL: https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume-26/issue-1/Exact-Penalization-and-Optimality-Conditions-for-Approximate-Directional-Minima/10.11650/tjm/211004.pdf
https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/advance-publication/Exact-Penalization-and-Optimality-Conditions-for-Approximate-Directional-Minima/10.11650/tjm/211004.full

On the directional asymptotic approach in optimization theory Part A: approximate, M-, and mixed-order stationarity

Authors: Benko, Matús Mehlitz, Patrick

Subject Terms: math.OC, 49J52, 49J53, 49K27, 90C22, 90C30, 90C33, 101016 Optimisation, 49K27, 0211 other engineering and technologies, 90C30, 02 engineering and technology, 90C22, 90C33, 101015 Operations Research, Optimization and Control (math.OC), 101015 Operations research, FOS: Mathematics, 101016 Optimierung, 49J52, Mathematics - Optimization and Control, 49J53

Access URL: http://arxiv.org/abs/2204.13932

Optimization of the Dirichlet problem for gradient differential inclusions.

Authors: Mahmudov, Elimhan N. Mastaliyeva, Dilara

Source: NoDEA: Nonlinear Differential Equations & Applications; Mar2024, Vol. 31 Issue 2, p1-20, 20p

Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems.

Authors: Long, X. J. Li, X. B. Zeng, J.

Source: Optimization Letters; Dec2013, Vol. 7 Issue 8, p1847-1856, 10p

Optimality conditions for various efficient solutions involving coderivatives: From set-valued optimization problems to set-valued equilibrium problems

Authors: Ha, Truong Xuan Duc¹ txdha@math.ac.vn

Source: Nonlinear Analysis. Feb2012, Vol. 75 Issue 3, p1305-1323. 19p.

Subject Terms: *SET-valued maps, *MATHEMATICAL optimization, *ASPLUND spaces, *BANACH spaces, *GLOBAL analysis (Mathematics), *VARIATIONAL inequalities (Mathematics), *VECTOR valued functions