A Lyusternik–Graves theorem for the proximal point method
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DOI: 10.1007/s10589-011-9439-6
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- R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
- Teemu Pennanen, 2002. "Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 170-191, February.
- Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
- Zhenhua Yang & Bingsheng He, 2005. "A Relaxed Approximate Proximal Point Algorithm," Annals of Operations Research, Springer, vol. 133(1), pages 119-125, January.
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Keywords
Proximal point algorithm; Generalized equations; Perturbations; Metric regularity; Strong regularity;All these keywords.
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