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1. Full Text Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings
by Gutiérrez, C and Huerga, L and Novo, V and Thibault, L
Set-Valued and Variational Analysis, ISSN 0927-6947, 06/2017, Volume 25, Issue 2, pp. 383 - 403
In this paper, several sequential formulae are obtained for the Brondsted-Rockafellar epsilon-subdifferential of the sum and the composition of two convex and... 
ε-subdifferential | Benson (C,ε)-proper subdifferential | p-regularly ε-subdifferentiable vector mapping | Sequential ε-subdifferential calculus | q-strong subdifferential | Brøndsted-Rockafellar theorem | epsilon-subdifferential | MATHEMATICS, APPLIED | Brondsted-Rockafellar theorem | CONVEX-FUNCTIONS | QUALIFICATION | p-regularly epsilon-subdifferentiable vector mapping | BANACH-SPACES | PROPER APPROXIMATE SOLUTIONS | Sequential epsilon-subdifferential calculus | OPTIMIZATION | Benson (C, epsilon)-proper subdifferential | OPTIMALITY | Mathematics
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2. Full Text On the Dini-Hadamard subdifferential of the difference of two functions
by Boţ, Radu Ioan and Nechita, Delia-Maria
Journal of Global Optimization, ISSN 0925-5001, 7/2011, Volume 50, Issue 3, pp. 485 - 502
In this paper we first provide a general formula of inclusion for the Dini-Hadamard ε-subdifferential of the difference of two functions and show that it... 
Fréchet ε -subdifferential | Cone-constrained nonsmooth nonconvex optimization problems | Optimality conditions in subdifferential form | Dini-Hadamard ε -subdifferential | Optimization | Economics / Management Science | Directionally approximately starshaped functions | 49J52 | Operations Research/Decision Theory | 90C56 | Sponge | Approximately starshaped functions | 26B25 | Computer Science, general | Real Functions | Dini-Hadamard ε-subdifferential | Fréchet ε-subdifferential | MATHEMATICS, APPLIED | APPROXIMATE SUBDIFFERENTIALS | Frechet epsilon-subdifferential | SPACES | CALCULUS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBGRADIENTS | Cone-constrained nonsmooth nonconvex optimization problems Optimality conditions in subdifferential form | Dini-Hadamard epsilon-subdifferential | GRADIENTS | Computer science | Universities and colleges | Studies | Mathematical problems
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3. Full Text Proper approximate solutions and ε-subdifferentials in vector optimization: Basic properties and limit behaviour
by Gutiérrez, C and Huerga, L and Jiménez, B and Novo, V
Nonlinear Analysis, ISSN 0362-546X, 03/2013, Volume 79, Issue 1, pp. 52 - 67
The aim of this work is to introduce a proper -subdifferential in the sense of Benson for extended mappings between topological linear spaces. It is defined by... 
Proper [formula omitted]-subdifferential | Linear scalarization | Proper [formula omitted]-efficiency | Nearly subconvexlikeness | [formula omitted]-subdifferential | Vector optimization | ε-subdifferential | Proper ε-subdifferential | Proper ε-efficiency | Proper epsilon-efficiency | epsilon-subdifferential | MATHEMATICS, APPLIED | Proper epsilon-subdifferential | CONES | CALCULUS | MATHEMATICS | RESPECT | SCALARIZATION | OPTIMALITY CONDITIONS | POINTS | EFFICIENCY
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4. Full Text Formulae for the Conjugate and the Subdifferential of the Supremum Function
by Pérez-Aros, Pedro
Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2019, Volume 180, Issue 2, pp. 397 - 427
This paper aims at providing some formulae for the subdifferential and the conjungate function of the supremum function over an arbitrary family of functions.... 
Pointwise supremum function | Mathematics | Theory of Computation | Optimization | Calculus of Variations and Optimal Control; Optimization | varepsilon $$ ε -Subdifferential | 90C25 | Operations Research/Decision Theory | 90C34 | Applications of Mathematics | Engineering, general | Fenchel conjugate | 46N10 | Convex analysis | ε-Subdifferential | MATHEMATICS, APPLIED | SET | CALCULUS RULES | FENCHEL SUBDIFFERENTIALS | EPSILON-SUBDIFFERENTIALS | EPI-POINTED FUNCTIONS | MINIMAX | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | epsilon-Subdifferential | INTEGRATION | CONVEX | PROPER APPROXIMATE SOLUTIONS | Employee motivation | Analysis
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5. Time-dependent subdifferential evolution inclusions and optimal control
by Hu, Shouchuan and Papageorgiou, Nikolaos Socrates and American Mathematical Society
1998, Memoirs of the American Mathematical Society, ISBN 082180779X, Volume no. 632., viii, 81
Subdifferentials | Differential inclusions | Evolution equations | Control theory | Mathematical optimization
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6. Subgradients of minimal time functions without calmness
by Nam, Nguyen Mau and Van Cuong, Dang
Journal of Convex Analysis, ISSN 0944-6532, 2019, Volume 26, Issue 1, pp. 189 - 200
Limiting subdifferential | Calmness | Singular subdifferential | ε-Fréchet subdifferential | Minimal time function
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7. Full Text Limiting subdifferentials of perturbed distance functions in Banach spaces
by Meng, Li and Li, Chong and Yao, Jen-Chih
Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1483 - 1495
We explore in arbitrary Banach spaces the Fréchet type -subdifferentials and the limiting subdifferentials for the perturbed distance function determined by a... 
Limiting subdifferential | Perturbed optimization problem | Subdifferential | [formula omitted]-subdifferential | Well-posedness | ε-subdifferential | epsilon-subdifferential | NONCONVEX OPTIMIZATION | EXISTENCE | POROSITY | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | DIFFERENTIABILITY | PRINCIPLE | MATHEMATICS | SETS | POINTS | Nonlinearity | Banach space | Estimates | Constraining
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8. Full Text An Additive Subfamily of Enlargements of a Maximally Monotone Operator
by Burachik, Regina S and Martínez-Legaz, Juan Enrique and Rezaie, Mahboubeh and Théra, Michel
Set-Valued and Variational Analysis, ISSN 1877-0533, 12/2015, Volume 23, Issue 4, pp. 643 - 665
We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These... 
Fitzpatrick function | Subdifferential operator | Enlargement of an operator | Brøndsted- Rockafellar enlargements | Mathematics | ε -subdifferential mapping | Convex lower semicontinuous function | Additive enlargements | Geometry | Maximally monotone operator | 90C30 | 90C46 | 49J52 | 90C25 | Analysis | Brøndsted- Rockafellar property | Fenchel-Young function | 48N15 | ε-subdifferential mapping | MATHEMATICS, APPLIED | REPRESENTATIONS | BUNDLE METHODS | PROOF | EXTENSION | EPSILON-ENLARGEMENTS | CONVEX-FUNCTIONS | FAMILY | Brondsted-Rockafellar property | epsilon-subdifferential mapping | Brondsted-Rockafellar enlargements | CONVERGENCE | Optimization and Control
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9. Full Text On the subdifferential of symmetric convex functions of the spectrum for symmetric and orthogonally decomposable tensors
by Chrétien, Stéphane and Wei, Tianwen
Linear Algebra and Its Applications, ISSN 0024-3795, 04/2018, Volume 542, pp. 84 - 100
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic... 
Tensor | Schatten norm | Subdifferential | Spectrum
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10. Integration of nonconvex epi-pointed functions in locally convex spaces
by Correa, Rafael and Hantoute, Abderrahim and Salas, David
Journal of Convex Analysis, ISSN 0944-6532, 2016, Volume 23, Issue 2, pp. 511 - 530
We extend the results of Correa, Garcia and Hantoute [6], dealing with the integration of nonconvex epi-pointed functions using the Fenchel subdifferential. In... 
MATHEMATICS | SUBDIFFERENTIALS
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11. Full Text Subdifferentiable functions satisfy Lusin properties of class C1 or C2
by Azagra, D and Ferrera, J and García-Bravo, M and Gómez-Gil, J
Journal of Approximation Theory, ISSN 0021-9045, 06/2018, Volume 230, pp. 1 - 12
Let be a function. Assume that for a measurable set and almost every there exists a vector such that Then we show that satisfies a Lusin-type property of order... 
Proximal subdifferential | Lusin property of order 2 | Fréchet subdifferential
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12. Full Text Necessary optimality conditions for a nonsmooth semi-infinite programming problem
by Gadhi, Nazih Abderrazzak
Journal of Global Optimization, ISSN 0925-5001, 2019, Volume 74, Issue 1, pp. 161 - 168
The nonsmooth semi-infinite programming (SIP) is solved in the paper (Mishra et al. in J Glob Optim 53:285-296, 2012) using limiting subdifferentials. The... 
Extremal principle | Optimality conditions | Limiting subdifferential | Constraint qualification | Fréchet subdifferential | Fréchet normal cone | Limiting normal cone | Nonsmooth semi-infinite optimzation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Frechet subdifferential | Frechet normal cone | Economic models | Nonlinear programming | Constraining
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13. Full Text The Fréchet and limiting subdifferentials of integral functionals on the spaces L1 (Ω, E)
by Chieu, Nguyen Huy
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2009, Volume 360, Issue 2, pp. 704 - 710
A new approach to computing the Fréchet subdifferential and the limiting subdifferential of integral functionals is proposed. Thanks to this way, we obtain... 
spaces | Fenchel subdifferential | Integral functional | Limiting subdifferential | Fréchet subdifferential
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14. Full Text ε -Subdifferential as an Enlargement of the Subdifferential
by Rezaie, Mahboubeh and Mirsaney, Zahra Sadat
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 10/2018, Volume 44, Issue 5, pp. 1283 - 1294
This work introduces a remarkable property of enlargements of maximal monotone operators. The basic tool in our analysis is a family of enlargements,... 
Weak | Subdifferential | ε-Subdifferential | lower semicontinuity | Enlargement | MATHEMATICS | epsilon-Subdifferential | MAXIMAL MONOTONE-OPERATORS | Weak-lower semicontinuity | CALCULUS | CONVEX-FUNCTIONS | FAMILY
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15. Full Text On Optimality Conditions for Henig Efficiency and Superefficiency in Vector Equilibrium Problems
by Luu, Do Van and Mai, Tran Thi
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 12/2018, Volume 39, Issue 16, pp. 1833 - 1854
Necessary optimality conditions for local Henig efficient and superefficient solutions of vector equilibrium problems involving equality, inequality, and set... 
Clarke subdifferential | 90C46 | Michel-Penot subdifferential | 49J52 | vector equilibrium problems | vector optimization problems | vector variational inequalities | local superefficient solutions | local Henig efficient solutions | 91B50 | Michel–Penot subdifferential | MATHEMATICS, APPLIED | CALCULUS | Banach space | Convexity | Nonlinear programming
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16. Full Text Chain Rules for a Proper ε-Subdifferential of Vector Mappings
by Gutiérrez, César and Huerga, Lidia and Novo, Vicente and Thibault, Lionel
Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2015, Volume 167, Issue 2, pp. 502 - 526
In this paper, we derive exact chain rules for a proper epsilon-subdifferential in the sense of Benson of extended vector mappings, recently introduced by... 
Proper ε-subdifferential | Strong ε-efficiency | Nearly cone-subconvexlikeness | Proper ε-efficiency | Strong ε-subdifferential | Linear scalarization | Vector optimization | Proper epsilon-efficiency | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | Proper epsilon-subdifferential | Strong epsilon-subdifferential | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMALITY CONDITIONS | POINTS | Strong epsilon-efficiency | Mathematics
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17. Full Text Second-order subdifferentials and convexity of real-valued functions
by Chieu, N.H and Huy, N.Q
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 1, pp. 154 - 160
In this paper we show that the positive semi-definiteness (PSD) of the Fréchet and/or Mordukhovich second-order subdifferentials can recognize the convexity of... 
Positive semi-definite property | Convexity | Mordukhovich second-order subdifferential | Fréchet second-order subdifferential | Frchet second-order subdifferential | MATHEMATICS | MATHEMATICS, APPLIED | Frechet second-order subdifferential | STABILITY
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18. Full Text Subdifferential estimate of the directional derivative, optimality criterion and separation principles
by Jules, Florence and Lassonde, Marc
Optimization, ISSN 0233-1934, 09/2013, Volume 62, Issue 9, pp. 1267 - 1288
We provide an inequality relating the radial directional derivative and the subdifferential of proper lower semicontinuous functions, which extends the known... 
subdifferential | maximal monotonicity | lower semicontinuity | directional derivative | mean value inequality | ϵ-subdifferential | optimality criteria | separation principle | ε{lunate}-subdifferential | LOWER SEMICONTINUOUS FUNCTIONS | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | E-subdifferential | 26D10 | SPACES | CONVEX-FUNCTIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 49J52 | SUBGRADIENTS | 26B25 | 49K27 | Separation | Approximation | Equivalence | Inequalities | Derivatives | Criteria | Banach space | Optimization | Mathematics | Optimization and Control
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19. Full Text Generalised-prox-regularity in reflexive smooth Banach spaces with smooth dual norm
by Bounkhel, Messaoud and Bachar, Mostafa
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2019, Volume 475, Issue 1, pp. 699 - 729
In this paper, we continue the study of the properties of the generalised projection on nonconvex sets in reflexive smooth Banach spaces with smooth dual norm... 
V-proximal subdifferential | Limiting V-proximal subdifferential | Generalised prox-regularity | V-proximal normal cone | Generalised projection | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIABILITY | SETS
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20. Full Text On the “bang-bang” principle for nonlinear evolution hemivariational inequalities control systems
by Bin, Maojun and Liu, Zhenhai
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2019, Volume 480, Issue 1, p. 123364
The purpose of this paper is to discuss the control systems of nonlinear evolution hemivariational inequalities and their “bang-bang” principle in Banach... 
Extremal trajectory | “Bang-bang” principle | Generalized Clarke subdifferential | Hemivariational inequalities
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