Coderivatives and the Solution Map of a Linear Constraint System
Duong Thi Kim Huyen, Nguyen Dong Yen · SIAM Journal on Optimization · 2016
The Lipschitz-like property and the metric regularity in the sense of Robinson of the solution map of a parametric linear constraint system are investigated thoroughly by means of normal coderivative, the Mordukhovich criterion, and a related theorem due to Levy and Mordukhovich [Math. Program., 99 (2004), pp. 311--327]. Among other things, the obtained results yield uniform local error bounds and traditional local error bounds for the linear complementarity problem and the general affine variational inequality problem, as well as verifiable sufficient conditions for the Lipschitz-like property of the solution map of the linear complementarity problem and a class of affine variational inequalities, where all components of the problem data are subject to perturbations.