- Title
- Calmness modulus of linear semi-infinite programs
- Creator
- Cánovas, Maria; Kruger, Alexander; López, Marco; Parra, Juan; Théra, Michel
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44315
- Identifier
- vital:5855
- Identifier
-
https://doi.org/10.1137/130907008
- Abstract
- 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.
- Publisher
- Society for Industrial and Applied Mathematics Publications
- Relation
- SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 29-48; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- © 2014, Society for Industrial and Applied Mathematics
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Calmness modulus; Isolated calmness; Linear programming; Semi-infinite programming; Variational analysis; Computer science; Software engineering; Constrained problem; Linear semi-infinite optimizations; Objective functions; Semi infinite programming; Semi-infinite programs; Mapping
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