On constant-level set constrained robust multi-dimensional controlled models

This paper investigated a new family of robust multidimensional controlled models with constant-level set constraints. More precisely, we considered the extremization of a functional, given by a controlled multiple integral involving an uncertain parameter, subject to a finite set of constraints determined by path-independent curvilinear integral functionals. Necessary and sufficient optimality criteria were established for a robust feasible point. In addition, a saddle-point-type characterization of robust optimal points was studied in the second part of the paper.