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Our main goal is to compute or estimate the calmness modulus of the argminmapping of linear semi-infinite optimization problems under canonicalperturbations, i.e., perturbations of the objective function together withcontinuous perturbations of the right-hand-side of the constraint system (withrespect to an index ranging in a compact Hausdorff space). Specifically, weprovide a lower bound on the calmness modulus for semi-infinite programs withunique optimal solution which turns out to be the exact modulus when theproblem is finitely constrained. The relationship between the calmness of theargmin mapping and the same property for the (sub)level set mapping (withrespect to the objective function), for semi-infinite programs and withoutrequiring the uniqueness of the nominal solution, is explored too, providing anupper bound on the calmness modulus of the argmin mapping. When confined tofinitely constrained problems, we also provide a computable upper bound as itonly relies on the nominal data and parameters, not involving elements in aneighborhood. Illustrative examples are provided.

Calmness modulus of linear semi-infinite programs