Journal of Inequalities and Applications (Oct 2023)

Second-order optimality conditions for interval-valued functions

  • Gabriel Ruiz-Garzón,
  • Rafaela Osuna-Gómez,
  • Antonio Rufián-Lizana,
  • Antonio Beato-Moreno

DOI
https://doi.org/10.1186/s13660-023-03054-5
Journal volume & issue
Vol. 2023, no. 1
pp. 1 – 19

Abstract

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Abstract This work is included in the search of optimality conditions for solutions to the scalar interval optimization problem, both constrained and unconstrained, by means of second-order optimality conditions. As it is known, these conditions allow us to reject some candidates to minima that arise from the first-order conditions. We will define new concepts such as second-order gH-derivative for interval-valued functions, 2-critical points, and 2-KKT-critical points. We obtain and present new types of interval-valued functions, such as 2-pseudoinvex, characterized by the property that all their second-order stationary points are global minima. We extend the optimality criteria to the semi-infinite programming problem and obtain duality theorems. These results represent an improvement in the treatment of optimization problems with interval-valued functions.

Keywords