Asymptotic Analysis of Perturbed Mathematical Programs

AbstractWe 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 ϵ. The following question arises: what is the description of the solutions of such a perturbed problem when ϵ→0? We demonstrate that, under weak conditions, the solutions of the perturbed problems are obtained as Puiseux series expansions in ϵ. The results are obtained by application of the Remmert–Stein representation theorem for complex analytic varieties