On First- and Second-Order Conditions for Error Bounds
Liren Huang, K. F. Ng · SIAM Journal on Optimization · 2004
We establish first-order and second-order sufficient conditions ensuring that a proper lower semicontinuous function f on a Banach space X has an error bound. We also consider similar problems with constraint, namely, that f is replaced by its restriction to a subset of X. These results are employed to identify exactly when a quadratic function on X has an error bound.