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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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Jg. 29; H. 3; S. 33
Hauptverfasser: Dhingra, Nidhi Arora, Lalitha, C. S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.07.2025
Springer Nature B.V
Schlagworte:
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.
Author_xml – sequence: 1
  givenname: Nidhi Arora
  surname: Dhingra
  fullname: Dhingra, Nidhi Arora
  organization: Department of Mathematics, Ramjas College, University of Delhi
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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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The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
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Issue 3
Keywords Discrete integral domain
Normal cones
Optimality conditions
Subdifferentials
90C46
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Convex analysis
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Language English
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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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