Generalized third-order conditions for error bound of proper functions in banach spaces

Time: 2019-06-18 17:36:44

        Using the second order directional derivatives, a generalized third order sumcient condition that can ensure an error bound fbr a proper continuous fhnction in a Banach space is established for the first time. The condition is based on the relevant first and second order sufficient conditions and makes it possible to ensure the existence of an error bound in cases where the first or second order sufficient conditions fail to work.

References：

1. Lulin Tan, Jing Mei, Qi Ye, Liren Huang. Generalized third-order conditions for error bound of proper functions in banach spaces. Journal of South China Normal University, 50(5), 106-109, 2018 (Chinese). DOI: 10.6054/j.jscnun.2018105