Asymptotic Analysis of Perturbed Mathematical Programs1

We consider a perturbed mathematical programming problem where both the objective and the constraint functions are analytical in both the underlying decision variables and in the perturbation variable/parameter that is denoted by . The following question arises: what is the description of the solutions of such a perturbed problem when → 0? We demonstrate that, under weak conditions, the solutions of the perturbed problems are obtained as Puiseux series expansions in . The results are obtained by application of the Remmert–Stein representation theorem for complex analytic varieties.