Best Approximate Solutions of Inconsistent Linear Inequality Systems

This paper is intended to characterize three types of best approximate solutions for inconsistent linear inequality systems with an arbitrary number of constraints. It also gives conditions guaranteeing the existence of best uniform solutions and discusses potential applications.This work was partially supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and by the Australian Research Council, Project DP160100854