Hölder continuity of perturbed solution set for convex optimization problems

In this paper, we first establish sufficient conditions for the local uniqueness and Hölder continuity of perturbed solution set for a scalar optimization problem. Then, by using a linear scalarization method, we obtain the Hölder continuity of two classes of perturbed solution sets for a multiobjective programming problem, respectively. We also give some examples to illustrate that our main results are applicable. These examples are also given to illustrate that our main results are new and different from the ones in literature.