Abstract
The stability of error bounds is significant in optimization theory and applications. Based on either the linearity assumption or the convexity and finite dimension assumption, several authors have focused on perturbation analysis of error bounds and obtained valuable results. Mainly motivated by Ngai, Kruger, and Thera [SIAM J. Optim., 20 (2010), pp. 2080-2096], in a general Banach space, we study the stability of error bounds for inequalities determined by proper lower semicontinuous quasi-subsmooth functions which are a very large class of nonconvex functions (in particular, approximate convex functions, primal-lower-nice functions, and convexly composite functions satisfying the Robinson qualification). We also consider the stability of error bounds for infinite constraint systems determined by infinitely many uniformly quasi-subsmooth functions. In particular, we extend the main results of Ngai, Kruger, and Thera to the infinite dimensional and nonconvex setting.
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