In this article, the second-order optimality conditions for nonlinear programming
with multiple interval-valued objective functions (in brief,
NPMIOF) are studied. In the first part, the second- and first-order necessary
optimality conditions for some types of efficient solutions of NPMIOF
are established under of Abadie second- and first-order constraint qualifications.
In the next part, we investigate both primal and dual secondorder
sufficient optimality conditions. Our second-order necessary conditions
enhance the previous results. The second-order sufficient optimality
conditions are new.