Abstract
In this paper, we consider approximate solutions (also called
$\varepsilon$-solutions) for semi-infinite optimization
problems that objective function and constraint functions with
uncertainty data are all convex, and establish robust counterpart of
convex semi-infinite program and then consider approximate solutions for
its. Moreover, the robust necessary condition and robust sufficient
theorems are obtained. Then the duality results of the Lagrangian dual
approximate solution is given by the robust optimization approach under
a cone constraint qualification.