Existence and optimality of accessible and approximatable minimizers of quasi upper robust functions

The concepts of robustness of sets and functions were proposed for the theory of integral global optimization which ensure that a robust minimizer can be approximated by a sequence of points at which the objective function is continuous. These concepts are generalized in this paper and global minimization of quasi upper robust functions is investigated. With the integral optimality conditions of global minimum, we examine existence of robust, accessible, and approximatable minimizers of discontinuous functions.