Subdifferential calculus in abstract convex cones

In this paper a new special class of separable normed cones is selected by us. This class includes cones in normed spaces as well as cones in linear spaces with asymmetric norms. Examples of separable normed cones that do not admit a linear injective isometric embedding in a normed space are given. In the class of separable normed cones the concept of compact subdifferential is introduced. The main properties of compact subdifferentials are studied in separable normed cones. Applications to some analogue of the well-known Fermat-Torricelli-Steiner problem are considered.