Local smooth representations of parametric semiclosed polyhedra with applications to sensitivity in piecewise linear programs (Q1935266)

The authors establish the equivalence between the representation of a smooth parametric semiclosed polyhedron by half-spaces and its representation by vertices. An application is given to study the sensitivity of a parametric piecewise linear problem. Namely, it is proved that the solution set of a parametric piecewise linear problem can be represented as a finite union of semiclosed polyhedra determined by smooth functions whenever the data of the problem smoothly depend on the parameter.