Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces
Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces is a scholarly work, published in 2018 in ''SIAM Journal on Optimization''. The main subjects of the publication include differentiable function, mathematical analysis, pure mathematics, iterative numerical method, upper and lower bounds, Lipschitz function, Fractional Laplacian, convex function, Banach space, biological function, regular polygon, algorithmic stability, applied mathematics, mathematics, perturbation, and contact mechanics. The authors 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 $E$.