SIP: critical value functions have finite modulus of non-convexity

SIP: critical value functions have finite modulus of non-convexity

We consider semi-infinite programming problems depending on a finite dimensional parameter . Provided that is a strongly stable stationary point of , there exists a locally unique and continuous stationary point mapping . This defines the local critical value function , where denotes the objective f...

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Veröffentlicht in:Mathematical programming 2012-12, Vol.136 (1), p.133-154
Hauptverfasser: Dorsch, D., Guerra-Vázquez, F., Günzel, H., Jongen, H. Th, Rückmann, J.-J.
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Exact sciences and technology
Full Length Paper
Graphs
Mapping
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Programming
Studies
Theoretical
Vectors (mathematics)
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Zusammenfassung:We consider semi-infinite programming problems depending on a finite dimensional parameter . Provided that is a strongly stable stationary point of , there exists a locally unique and continuous stationary point mapping . This defines the local critical value function , where denotes the objective function of for a given parameter vector . We show that is the sum of a convex function and a smooth function. In particular, this excludes the appearance of negative kinks in the graph of .
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-012-0554-7