Publication: Optimization methods and stability of inclusions in Banach Spaces
Optimization methods and stability of inclusions in Banach Spaces
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Klatte, D., & Kummer, B. (2009). Optimization methods and stability of inclusions in Banach Spaces. Mathematical Programming, 117, 305–330. https://doi.org/10.1007/s10107-007-0174-9
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Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which requi
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- Klatte, Diethard
- Kummer, Bernd
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Klatte, D., & Kummer, B. (2009). Optimization methods and stability of inclusions in Banach Spaces. Mathematical Programming, 117, 305–330. https://doi.org/10.1007/s10107-007-0174-9
