Lipschitz lower semicontinuity is a quantitative stability property for set-valued maps with relevant applications to perturbation analysis of optimization problems. The present paper reports on an attempt of studying such property, by starting with a related result valid for variational systems in metric spaces. Elements of nonsmooth analysis are subsequently employed to express and apply such result and its consequences in more structured settings. This approach leads to obtain a solvability, stability, and sensitivity condition for perturbed optimization problems with quasidifferentiable data.
Uderzo, A. (2014). On a Quantitative Semicontinuity Property of Variational Systems with Applications to Perturbed Quasidifferentiable Optimization. In V.F. Demyanov, P.M. Pardalos, M. Batsyn (a cura di), Constructive Nonsmooth Analysis and Related Topics (pp. 115-136). Springer International Publishing [10.1007/978-1-4614-8615-2_8].
On a Quantitative Semicontinuity Property of Variational Systems with Applications to Perturbed Quasidifferentiable Optimization
UDERZO, AMOSPrimo
2014
Abstract
Lipschitz lower semicontinuity is a quantitative stability property for set-valued maps with relevant applications to perturbation analysis of optimization problems. The present paper reports on an attempt of studying such property, by starting with a related result valid for variational systems in metric spaces. Elements of nonsmooth analysis are subsequently employed to express and apply such result and its consequences in more structured settings. This approach leads to obtain a solvability, stability, and sensitivity condition for perturbed optimization problems with quasidifferentiable data.
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