Search Results - coderivatives of set-valued maps

Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization

Authors: Xiaowei Xue

Source: Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-15 (2020)

Subject Terms: Parametric vector optimization, Efficient point set-valued map, Efficient solution set-valued map, (Fréchet) coderivative, Aubin property, Mathematics, QA1-939

File Description: electronic resource

Relation: http://link.springer.com/article/10.1186/s13660-020-02499-2; https://doaj.org/toc/1029-242X

Access URL: https://doaj.org/article/5dc36d59bb2a4e689ea823b3f88ae296

The Ekeland variational principle for set-valued maps involving coderivatives

Authors: Truong Xuan Duc Ha

Source: Journal of Mathematical Analysis and Applications. 286:509-523

Subject Terms: coderivative, set-valued map, optimality condition, Applied Mathematics, Marginal function, Nonsmooth analysis, 0211 other engineering and technologies, Ekeland's variational principle, Set-valued map, Optimality condition, 02 engineering and technology, 01 natural sciences, marginal function, Coderivative, 0101 mathematics, Analysis, Set-valued and variational analysis

File Description: application/xml

Access URL: https://zbmath.org/2006341
https://doi.org/10.1016/s0022-247x(03)00482-7
https://www.sciencedirect.com/science/article/pii/S0022247X03004827
https://www.sciencedirect.com/science/article/abs/pii/S0022247X03004827

SENSITIVITY ANALYSIS OF PARAMETRIC VECTOR SET-VALUED OPTIMIZATION PROBLEMS VIA CODERIVATIVES

Authors: Xue, X. W. Li, S. J. Liao, C. M. et al.

Source: Taiwanese Journal of Mathematics, 2011 Dec 01. 15(6), 2533-2554.

Access URL: https://www.jstor.org/stable/taiwjmath.15.6.2533

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

Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps

Authors: A. D. Ioffe

Source: Nonlinear Analysis: Theory, Methods & Applications. 8:517-539

Subject Terms: Optimality conditions, Derivatives of functions in infinite-dimensional spaces, Methods involving semicontinuity and convergence, relaxation, Lipschitz mapping, equivalent Gâteaux differentiable norm, Convex sets in topological linear spaces, Choquet theory, contingent coderivative of a set- valued map, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, Nonlinear programming, lower Dini directional derivative, Dini subdifferential, Lagrange multipler rule, 0101 mathematics, generalized derivatives

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/0362546X84900919

Some Variants of the Ekeland Variational Principle for a Set-Valued Map: Some variants of the Ekeland variational principle for a set-valued map

Authors: Truong Xuan Duc Ha

Source: Journal of Optimization Theory and Applications. 124:187-206

Subject Terms: set-valued maps, Nonsmooth analysis, 0211 other engineering and technologies, Ekeland variational principle, 02 engineering and technology, stability, 0101 mathematics, Mordukhovich coderivatives, 01 natural sciences, Set-valued and variational analysis

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s10957-004-6472-y
https://dl.acm.org/doi/10.1007/s10957-004-6472-y

Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone

Authors: Truong Xuan Duc Ha

Source: Journal of Mathematical Analysis and Applications. 316:346-356

Subject Terms: Clarke's normal cone, Vector optimization, Applied Mathematics, 0211 other engineering and technologies, Ekeland's variational principle, Set-valued map, 02 engineering and technology, Coderivative, 0101 mathematics, 01 natural sciences, Analysis

Access URL: https://www.sciencedirect.com/science/article/pii/S0022247X05003859
https://core.ac.uk/display/82549270
http://ui.adsabs.harvard.edu/abs/2006JMAA..316..346H/abstract

Lagrange multipliers for set-valued optimization problems associated with coderivatives

Authors: Truong Xuan Duc Ha

Source: Journal of Mathematical Analysis and Applications. 311:647-663

Subject Terms: vector optimization, set-valued map, Lagrange multipliers, Applied Mathematics, Nonsmooth analysis, 0211 other engineering and technologies, subdifferential, 02 engineering and technology, 01 natural sciences, Fréchet's coderivative, optimal solution, Mordukhovich's coderivative, marginal function, Optimality conditions and duality in mathematical programming, 0101 mathematics, Multi-objective and goal programming, Analysis, Set-valued and variational analysis

File Description: application/xml

Access URL: https://zbmath.org/2217438
https://doi.org/10.1016/j.jmaa.2005.03.011
https://www.sciencedirect.com/science/article/pii/S0022247X05002003
http://ui.adsabs.harvard.edu/abs/2005JMAA..311..647H/abstract

Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications.

Authors: Thinh, Vo Duc Qin, Xiaolong Yao, Jen-Chih

Source: Journal of Optimization Theory & Applications. Dec2024, Vol. 203 Issue 3, p2784-2817. 34p.

Subject Terms: *SET-valued maps, *EQUILIBRIUM

DIFFERENTIABILITY OF PROBABILITY FUNCTIONS INVOLVING STAR-SHAPED VALUED SET-VALUED MAPS.

Authors: VAN ACKOOIJ, WIM PEREZ-AROS, PEDRO SOTO, CLAUDIA

Source: SIAM Journal on Optimization; 2025, Vol. 35 Issue 2, p1216-1245, 30p

Subject Terms: LIPSCHITZ continuity, DISTRIBUTION (Probability theory), SET-valued maps, DIFFERENTIABLE functions, SUBDIFFERENTIALS, RANDOM variables

Sensitivity analysis of parametric vector equilibrium problems on Fréchet coderivative.

Authors: Deng, Xicai Liu, Yibo Zhong, Chongyi

Source: Journal of Inequalities & Applications; 11/17/2025, Vol. 2025 Issue 1, p1-12, 12p

Oriented Calmness and Sweeping Process Dynamics.

Authors: Daniilidis, Aris Tapia, Sebastian

Source: Mathematics of Operations Research. Aug2024, Vol. 49 Issue 3, p1472-1486. 15p.

Subject Terms: CALMNESS, SET-valued maps, ORBITS (Astronomy)

On the directional asymptotic approach in optimization theory: The directional asymptotic approach: M. Benko, P. Mehlitz.

Authors: Benko, Matúš Mehlitz, Patrick

Source: Mathematical Programming; Jan2025, Vol. 209 Issue 1, p859-937, 79p

Subject Terms: CALCULUS of variations, SEMIDEFINITE programming, SET-valued maps, MATHEMATICAL optimization, SENSES, NONSMOOTH optimization

Covering constants for metric projection operator with applications to stochastic fixed-point problems.

Authors: Li, Jinlu

Source: Journal of Global Optimization; Aug2025, Vol. 92 Issue 4, p993-1020, 28p

Subject Terms: METRIC projections, MATHEMATICAL optimization, STOCHASTIC programming, SET-valued maps, SUBDIFFERENTIALS, MATHEMATICAL constants, VARIATIONAL approach (Mathematics), BANACH spaces

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

CODERIVATIVES OF FRONTIER AND SOLUTION MAPS IN PARAMETRIC MULTIOBJECTIVE OPTIMIZATION

Authors: Huy, N. Q. Mordukhovich, B. S. Yao, J. C.

Source: Taiwanese J. Math. 12, no. 8 (2008), 2083-2111

Subject Terms: variational analysis, 90C29, generalized order and generalized Pareto optimality, Lipschitzian properties, 0211 other engineering and technologies, 90C30, frontier and efficient solution maps, set-valued mappings, coderivatives, 02 engineering and technology, 49J52, parametric multiobjective optimization, 49J53

File Description: application/pdf

Access URL: https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume-12/issue-8/CODERIVATIVES-OF-FRONTIER-AND-SOLUTION-MAPS-IN-PARAMETRIC-MULTIOBJECTIVE-OPTIMIZATION/10.11650/twjm/1500405137.short
https://projecteuclid.org/download/pdf_1/euclid.twjm/1500405137
https://projecteuclid.org/euclid.twjm/1500405137

A Notion of Fenchel Conjugate for Set-Valued Mappings.

Authors: Nam, Nguyen Mau Sandine, Gary Thieu, Nguyen Nang et al.

Source: Journal of Optimization Theory & Applications. Nov2024, Vol. 203 Issue 2, p1263-1292. 30p.

Subject Terms: *SET-valued maps, *GEOMETRIC approach, *CALCULUS, *INSPIRATION

ON METRIC PSEUDO-REGULARITY OF MULTIFUNCTIONS.

Authors: VAN VU NGUYEN HUU TRON NGUYEN

Source: Applied Set-Valued Analysis & Optimization; 2025, Vol. 7 Issue 1, p93-110, 18p

Subject Terms: MATHEMATICAL functions, SET-valued maps, BANACH spaces, VARIATIONAL principles, VECTOR spaces

Coderivatives of the generalized perturbation maps.

Authors: Xue, X. Li, S.

Source: Positivity. Jun2011, Vol. 15 Issue 2, p309-329. 21p.

Subject Terms: *MATHEMATICAL analysis, SET-valued maps, BANACH spaces, PERTURBATION theory, CALCULUS, DIFFERENTIABLE functions, MATHEMATICAL mappings

Strict Efficiency in Set Optimization Studied with the Set Approach.

Authors: Ha, Truong Xuan Duc¹ (AUTHOR) hatxd@thanglong.edu.vn

Source: Journal of Optimization Theory & Applications. May2025, Vol. 205 Issue 2, p1-20. 20p.

Subject Terms: *DIRECTIONAL derivatives, *SUBDIFFERENTIALS, *SET-valued maps