Metric Subregularity of Piecewise Linear Multifunctions and Applications to Piecewise Linear Multiobjective Optimization

In this paper, we consider the metric subregularity property for a piecewise linear multifunction (with respect to a piecewise linear constraint) as well as the weak sharp minimum property for a piecewise linear constrained multiobjective optimization problem. Of these properties we pay special attention to the global ones. We first provide a result on a certain relationship between two nonnegative piecewise linear numerical functions for which the kernel of one of them is contained in the kernel of the other. Using this result, we establish the bounded/global metric subregularity results for a piecewise linear multifunction with respect to a piecewise linear set. As applications, we study the weak sharp minimum property for a piecewise linear constrained multiobjective optimization problem.