Sensitivity analysis of the value function for optimization problems with variational inequality constraints

In this paper we perform sensitivity analysis for optimization problems wit h variational inequality constraints (OPVICs). We provide upper estimates f or the limiting subdifferential (singular limiting subdifferential) of the value function in terms of the set of normal (abnormal) coderivative (CD) m ultipliers for OPVICs. For the case of optimization problems with complemen tarity constraints (OPCCs), we provide upper estimates for the limiting sub differentials in terms of various multipliers. An example shows that the ot her multipliers may not provide useful information on the subdifferentials of the value function, while the CD multipliers may provide tighter bounds. Applications to sensitivity analysis of bilevel programming problems are a lso given.