  This paper deals with approximate solutions of a nonsmooth semi-infinite
programming with multiple interval-valued objective functions. We first
introduce four types of approximate quasi Pareto solutions of the considered
problem by considering the lower-upper interval order relation and then apply
some advanced tools of variational analysis and generalized differentiation to
establish necessary optimality conditions for these approximate solutions.
Sufficient conditions for approximate quasi Pareto solutions of such a problem
are also provided by means of introducing the concepts of approximate
(strictly) pseudo-quasi generalized convex functions defined in terms of the
limiting subdifferential of locally Lipschitz functions. Finally, a Mond--Weir
type dual model in approximate form is formulated, and weak, strong and
converse-like duality relations are proposed.
