Error Bounds for Convex Inequality Systems
By A. S. Lewis, Jong-Shi Pang. 1998
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Citations in the corpus
- Sufficient Conditions for Error Bounds and Applications (2004, background): “Remark 3. In the paper by Lewis and Pang [ 17 ], they gave conditions for the existence of a global error bound for a convex inequality system and established a necessary and sufficient condition for a closed convex set defined by a closed proper function to possess a global error bound in terms of ”
- Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties (2000, background): “These geometric properties are key in the study of various areas in convex optimization and bordering flelds, such as: Fenchel duality [13, 12]; duality for convex cones [19]; systems of convex inequalities and associated error bounds [ 22 , 23, 9]; projection algorithms and their rate of convergenc”
- Error Bounds: Necessary and Sufficient Conditions (2010, methodology): “We refer the interested reader to the surveys by Azé [1], Lewis and Pang [35], and Pang [44].”
- Characterizations of error bounds for lower semicontinuous functions on metric spaces (2004, background): “This result – in fact, the second equality – was established by Lewis and Pang in [19] (Th.”
- Strong CHIP, normality, and linear regularity of convex sets (2005, background): “Linear regularity is also related to error estimates for approximate solutions of a feasibility problem (such as Hoffman’s error bounds) [10, 30, 25].”
- New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors (2015, background): “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”