First and Second-Order Conditions for Interval Optimization Problems by Using Generalized Interval Differences

doi:10.1007/s10957-026-03005-2

First and Second-Order Conditions for Interval Optimization Problems by Using Generalized Interval Differences

2026-04-29

0

PRE

AI

Y

Y. Chalco-Cano

B

Beatriz Hernández‐Jiménez

A

Alberto Ramos *

DOI：10.1007/s10957-026-03005-2

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We investigate first- and second-order optimality conditions for constrained optimization problems with interval-valued objective functions. By introducing new directional derivatives based on generalized Hukuhara differences, we establish necessary and sufficient optimality conditions. The proposed conditions extend existing results and remain applicable even when the endpoint functions of the interval are nonsmooth or nonconvex. Important statements are illustrated by examples.

Keywords:

Interval optimization

Optimality conditions

Generalized Hukuhara differences

First and Second-Order Conditions for Interval Optimization Problems by Using Generalized Interval Differences

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