RELATIVE LIPSCHITZ-LIKE PROPERTY OF PARAMETRIC SYSTEMS VIA PROJECTIONAL CODERIVATIVES

This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The necessity is also obtainable under some regularity or when the polyhedral set is further the domain of the solution mapping. We further discuss possible conditions for the necessity and consider the solution mapping of a linear complementarity problem with a Q0 matrix as an example.

Automated summary

This paper investigates upper estimates of the projectional coderivative of implicit mappings and their applications in analyzing the relative Lipschitz-like property. The paper provides upper estimates of the projectional coderivative for solution mappings of parametric systems under different constraint qualifications. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained to determine the sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The necessity can also be obtained under certain regularity conditions or when the polyhedral set further becomes the domain of the solution mapping. Possible conditions for the necessity are further discussed, and a solution mapping of a linear complementarity problem with a Q0 matrix is considered as an example.