Discrete convex subdifferentials and optimality

The aim of the paper is to study the notions of normal cones and subdifferentials in the integral domain Z n and derive optimality conditions for an abstract set constrained problem in terms of normal cones and subdifferentials. Various properties and calculus rules of normal cones, subdifferentials...

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Vydáno v:Positivity : an international journal devoted to the theory and applications of positivity in analysis Ročník 29; číslo 3; s. 33
Hlavní autoři: Dhingra, Nidhi Arora, Lalitha, C. S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.07.2025
Springer Nature B.V
Témata:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Cones
Convex analysis
Econometrics
Fourier Analysis
Linear programming
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Discrete integral domain
Normal cones
Optimality conditions
Subdifferentials
90C46
90C25
46N10
Convex analysis
52C07
ISSN:1385-1292, 1572-9281
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Abstract The aim of the paper is to study the notions of normal cones and subdifferentials in the integral domain Z n and derive optimality conditions for an abstract set constrained problem in terms of normal cones and subdifferentials. Various properties and calculus rules of normal cones, subdifferentials and singular subdifferentials are established and the differences with existing analogous rules in the real domain R n are justified through counter examples.
AbstractList The aim of the paper is to study the notions of normal cones and subdifferentials in the integral domain Zn and derive optimality conditions for an abstract set constrained problem in terms of normal cones and subdifferentials. Various properties and calculus rules of normal cones, subdifferentials and singular subdifferentials are established and the differences with existing analogous rules in the real domain Rn are justified through counter examples.
The aim of the paper is to study the notions of normal cones and subdifferentials in the integral domain Z n and derive optimality conditions for an abstract set constrained problem in terms of normal cones and subdifferentials. Various properties and calculus rules of normal cones, subdifferentials and singular subdifferentials are established and the differences with existing analogous rules in the real domain R n are justified through counter examples.
ArticleNumber 33
Author Dhingra, Nidhi Arora
Lalitha, C. S.
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  givenname: C. S.
  surname: Lalitha
  fullname: Lalitha, C. S.
  email: cslalitha@maths.du.ac.in, cslalitha1@gmail.com
  organization: Department of Mathematics, University of Delhi South Campus
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Cites_doi 10.1137/19M1281678
10.1007/BF03323153
10.1137/0121018
10.1006/aima.1996.0084
10.1017/9781108699211
10.3934/jimo.2012.8.189
10.1007/BF01949705
10.1007/BF02680565
10.1007/s10107-016-1010-x
10.1007/BF03167496
10.1137/1.9780898718508
10.1137/22M1483165
10.1007/s40305-017-0158-2
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Issue 3
Keywords Discrete integral domain
Normal cones
Optimality conditions
Subdifferentials
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Convex analysis
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Language English
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References P Favati (1118_CR2) 1990; 53
B Mordukhovich (1118_CR17) 2023
K Murota (1118_CR4) 1996; 124
HH Bauschke (1118_CR15) 2023; 33
NZ Shor (1118_CR14) 2015
NK Vishnoi (1118_CR13) 2021
Š Damjan (1118_CR16) 2023; 158
T Ui (1118_CR5) 2006; 23
K Murota (1118_CR3) 1998; 83
B Mordukhovich (1118_CR18) 2022
K Murota (1118_CR7) 2003
BL Miller (1118_CR1) 1971; 21
S Hilger (1118_CR9) 1990; 18
M Adıvar (1118_CR10) 2012; 8
JM Borwein (1118_CR8) 2018; 168
J-P Doignon (1118_CR6) 1973; 3
M Adıvar (1118_CR11) 2018; 6
J Li (1118_CR12) 2020; 30
References_xml – volume: 30
  start-page: 2809
  issue: 4
  year: 2020
  ident: 1118_CR12
  publication-title: SIAM J. Optim.
  doi: 10.1137/19M1281678
– volume-title: Minimization methods for non-differentiable functions
  year: 2015
  ident: 1118_CR14
– volume: 158
  start-page: 21
  year: 2023
  ident: 1118_CR16
  publication-title: Internat J. Approx. Reason
– volume: 18
  start-page: 18
  year: 1990
  ident: 1118_CR9
  publication-title: Results. Math.
  doi: 10.1007/BF03323153
– volume: 21
  start-page: 166
  issue: 1
  year: 1971
  ident: 1118_CR1
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0121018
– volume: 124
  start-page: 272
  issue: 2
  year: 1996
  ident: 1118_CR4
  publication-title: Adv. Math.
  doi: 10.1006/aima.1996.0084
– volume-title: Algorithms for convex optimization
  year: 2021
  ident: 1118_CR13
  doi: 10.1017/9781108699211
– volume: 8
  start-page: 189
  issue: 1
  year: 2012
  ident: 1118_CR10
  publication-title: J. Ind. Manag. Optim.
  doi: 10.3934/jimo.2012.8.189
– volume: 53
  start-page: 3
  year: 1990
  ident: 1118_CR2
  publication-title: Ric. Oper.
– volume: 3
  start-page: 71
  issue: 1
  year: 1973
  ident: 1118_CR6
  publication-title: J. Geom.
  doi: 10.1007/BF01949705
– volume: 83
  start-page: 313
  year: 1998
  ident: 1118_CR3
  publication-title: Math. Program.
  doi: 10.1007/BF02680565
– volume: 168
  start-page: 11
  year: 2018
  ident: 1118_CR8
  publication-title: Math. Program.
  doi: 10.1007/s10107-016-1010-x
– volume: 23
  start-page: 21
  issue: 1
  year: 2006
  ident: 1118_CR5
  publication-title: Japan. J. Ind. Appl. Math.
  doi: 10.1007/BF03167496
– volume-title: An easy path to convex analysis and applications. Synthesis Lectures on Mathematics and Statistics
  year: 2023
  ident: 1118_CR17
– volume-title: Convex analysis and beyond, basic theory. Springer series in operations research and financial engineering
  year: 2022
  ident: 1118_CR18
– volume-title: Discrete convex analysis. siam monographs on discrete mathematics and applications
  year: 2003
  ident: 1118_CR7
  doi: 10.1137/1.9780898718508
– volume: 33
  start-page: 739
  issue: 2
  year: 2023
  ident: 1118_CR15
  publication-title: SIAM J. Optim.
  doi: 10.1137/22M1483165
– volume: 6
  start-page: 189
  year: 2018
  ident: 1118_CR11
  publication-title: J. Oper. Res. Soc. China
  doi: 10.1007/s40305-017-0158-2
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SubjectTerms Algorithms
Calculus of Variations and Optimal Control; Optimization
Cones
Convex analysis
Econometrics
Fourier Analysis
Linear programming
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Title Discrete convex subdifferentials and optimality
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