Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces
Chong Li, K. F. Ng · SIAM Journal on Optimization · 2018
Using the error bound results established in the present paper for approximate solutions, we study the stability issues when perturbed by possibly nonaffine smooth maps $E$ for the abstract inequality system $F\ge _K0$ defined by a (possible nonclosed) convex cone $K$ and a Fréchet differentiable function $F$ satisfying the (extended) weak $\gamma$-condition. We provide some sufficient conditions, in terms of the information at a solution $x_0$, for ensuring the lower semicontinuity and/or the Lipschitz-like continuity at $x_0$ of the solution mapping for the perturbed system $F+E\ge _K0$ with smooth perturbation $E$. Explicit upper bounds of the Lipschitz-like moduli are also provided.