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.Funding for open access publishing: Universidad de Cádiz/CBUA. The research has been supported by MCIN through
grant MCIN/AEI/PID2021-123051NB-I00
