Parametric semi-infinite programming problems: properties of solution functions

We study sensitivity and asymptotic behavior of solutions to parametric convex semi-infinite programming problems with compact polyhedral index sets. We analyze properties of optimal solutions, Lagrange multipliers, and active sets as the parameter approaches a nominal value. Under standard smoothness, convexity, and constraint qualification assumptions, we characterize the limits and first-order derivatives of the associated primal and dual mappings.