Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Relationship between static and dynamic elastic modulus of calcarenite heated at different temperatures: the San Julián's stone

The San Julián’s stone is the main material used to build the most important historical buildings in Alicante city (Spain). This paper describes the analysis developed to obtain the relationship between the static and the dynamic modulus of this sedimentary rock heated at different temperatures. The rock specimens have been subjected to heating processes at different temperatures to produce different levels of weathering on 24 specimens. The static and dynamic modulus has been measured for every specimen by means of the ISRM standard and ultrasonic tests, respectively. Finally, two analytic formulas are proposed for the relationship between the static and the dynamic modulus for this stone. The results have been compared with some relationships proposed by different researchers for other types of rock. The expressions presented in this paper can be useful for the analysis, using non-destructive techniques, of the integrity level of historical constructions built with San Julián’s stone affected by fires.