Change of generalized indices of stationary solutions to multiparametric optimization

We study the local change of the generalized index, which is a modification of the Morse index and the stationary index, for the multiparametric optimization. Under the Regular Value Condition, the change of the generalized index around a triplet (x, v, t) is locally bounded by the dimension of the parameter vector t, where x is a variable vector and v a vector of the Lagrange multiplier space. We also discuss the local change of the generalized index around a pair (x, t).