JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2024 (SCI-Expanded)
This paper provides formulas for calculating Fr & eacute;chet and limiting normal cones with respect to a set of sets and the limiting coderivative with respect to a set of set-valued mappings. These calculations are obtained under some qualification constraints and are expressed in the similar forms of the ones of Fr & eacute;chet and limiting normal cones and the limiting coderivative. By using these new formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some examples are also presented.