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

Fabiola Roxana Villanueva () and Valeriano Antunes Oliveira ()
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Fabiola Roxana Villanueva: Universidad Mayor de San Andrés
Valeriano Antunes Oliveira: São Paulo State University

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 7, 896-923

Abstract: Abstract 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).

Keywords: Interval optimization; Necessary optimality conditions; Karush–Kuhn–Tucker; Dubovitskii–Milyutin formalism; 90C70; 90C46; 90C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02055-6

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