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Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization. (English) Zbl 1430.49014

Summary: Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Hölder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Hölder calmness modulus of the argmin mapping in the framework of linear programming.

MSC:

49J53 Set-valued and variational analysis
90C25 Convex programming
90C31 Sensitivity, stability, parametric optimization
90C34 Semi-infinite programming
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