  In this paper, we mainly study one class of mixed-integer nonlinear
programming problems (MINLPs) with vector conic constraint in Banach spaces.
Duality theory of convex vector optimization problems applied to this class of
MINLPs is deeply investigated. With the help of duality, we use the generalized
Benders decomposition method to establish an algorithm for solving this MINLP.
Several convergence theorems on the algorithm are also presented. The
convergence theorems generalize and extend the existing results on MINLPs in
finite dimension spaces.
