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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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 29; no. 3; p. 33
Main Authors: Dhingra, Nidhi Arora, Lalitha, C. S.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.07.2025
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-025-01118-y