Isolated calmness of solution mappings in convex semi-infinite optimization |
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| Authors: | M.J. C novas, A.L. Dontchev, M.A. L pez,J. Parra |
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| Affiliation: | aOperations Research Center, Miguel Hernández University of Elche, 03202 Elche, Alicante, Spain;bNational Science Foundation, 4201 Wilson Boulevard, Arlington, VA 22230, USA;cDepartment of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain |
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| Abstract: | This paper is concerned with isolated calmness of the solution mapping of a parameterized convex semi-infinite optimization problem subject to canonical perturbations. We provide a sufficient condition for isolated calmness of this mapping. This sufficient condition characterizes the strong uniqueness of minimizers, under the Slater constraint qualification. Moreover, on the assumption that the objective function and the constraints are linear, we show that this condition is also necessary for isolated calmness. |
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| Keywords: | Isolated calmness Variational analysis Convex optimization Semi-infinite programming Strong uniqueness Sharp minima |
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