We are concerned with the Lipschitz modulus of the optimal set mapping
associated with canonically perturbed convex semi-infinite optimization
problems. Specifically, the paper provides a lower and an upper bound for
this modulus, both of them given exclusively in terms of the problem's data.
Moreover, the upper bound is shown to be the exact modulus when the number
of constraints is finite. In the particular case of linear problems the
upper bound (or exact modulus) adopts a notably simplified expression. Our
approach is based on variational techniques applied to certain difference of
convex functions related to the model. Some results of [M.J. Cánovas et al., J. Optim. Theory Appl. (2008) Online First]
(which go back to [M.J. Cánovas, J. Global Optim.
41 (2008) 1–13] and [Ioffe, Math. Surveys
55 (2000) 501–558; Control Cybern.
32 (2003) 543–554])
constitute the starting point of the present work.