Error Bounds: Necessary and Sufficient Conditions
By Marian J. Fabian, René Henrion, Alexander Y. Kruger, Jirí Vladimír Outrata. 2010
181 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/3ae239eb3aed0bec820dad555ada04267b71126c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Control and Systems Engineering
In Numerical Analysis
- Nicolas Loizou
- Robert Mansel Gower
- Othmane Sebbouh
- Alexander Y. Kruger
- Peter Richtárik
- Jakub Konecný
Citations in the corpus
- New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors (2015, unknown): “Keywords Error bounds · Polynomials · Variational analysis · Generalized differentiation · Łojasiewicz’s inequality · Hölderian stability · Polynomial optimization and complementarity Mathematics Subject Classification 90C26 · 90C31 · 49J52 · 49J53 · 26D10”
- SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and Interpolation (2020, background): “Such conditions include error bound properties (Fabian et al., 2010), essential strong convexity (Liu et al.”
- Error bounds and metric subregularity (2014, methodology): “Such an analogue of (12) is known as the strict slope [12] (limiting slope [5, 62, 63]); compare with the relaxed slope [30] and the strong relaxed slope [64].”
- Error Bounds and Hölder Metric Subregularity (2014, unknown): “, [2, 4, 13, 22]) with constant τ > 0 at a point x̄ ∈ X with f(x̄) = 0 if there exists a neighbourhood U of x̄ such that τd(x,S(f)) ≤ f+(x) for all x ∈ U.”