Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints

This work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional and abstract forms. The functional constraints are described by means of both inequalities and equalities. The abstract constraint is expressed through...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 194; no. 3; pp. 896 - 923
Main Authors: Villanueva, Fabiola Roxana, de Oliveira, Valeriano Antunes
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer Nature B.V
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Engineering
Inequality
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Interval optimization
Necessary optimality conditions
90C30
90C46
Karush–Kuhn–Tucker
Dubovitskii–Milyutin formalism
90C70
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional and abstract forms. The functional constraints are described by means of both inequalities and equalities. The abstract constraint is expressed through a closed and convex set with a nonempty interior. Necessary optimality conditions are derived, given in a multiplier rule structure involving the gH-gradient of the interval objective function along with the (classical) gradients of the constraint functions and the normal cone to the set related to the abstract constraint. The main tool is a specification of the Dubovitskii–Milyutin formalism. We defined an appropriated notion of directions of decrease to an interval-valued function, using the lower–upper partial ordering of the interval space (LU order).
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02055-6