  Generalized polyhedral convex sets, generalized polyhedral convex functions
on locally convex Hausdorff topological vector spaces, and the related
constructions such as sum of sets, sum of functions, directional derivative,
infimal convolution, normal cone, conjugate function, subdifferential, are
studied thoroughly in this paper. Among other things, we show how a generalized
polyhedral convex set can be characterized via the finiteness of the number of
its faces. In addition, it is proved that the infimal convolution of a
generalized polyhedral convex function and a polyhedral convex function is a
polyhedral convex function. The obtained results can be applied to scalar
optimization problems described by generalized polyhedral convex sets and
generalized polyhedral convex functions.
