Let $C$ be a convex set. A convex subset $F\subset C$ is called a face of $C$ if, for every closed line segment ${\overline{u_{1}u_{2}}}\subset C$ such that $\operatorname{ri}({\overline{u_{1}u_{2}}})\cap F\not=\emptyset$, the inclusion ${\overline{u_{1}u_{2}}}\subset F$ holds. A face of $C$ of codimension 1 is called a facet. A non-empty subset $F\subset C$ is called an exposed face of $C$ if there exists $x\in M_{\mathbb{R}}$ such that