Generalized inequality

A generalized inequality is defined in terms of a proper cone $$K$$ and is symbolized with the notation $$\preceq_K$$. The generalized inequality $$\preceq_K$$ is defined as

$$x \preceq_K y \implies y-x \in K$$.

A strict generalized inequality $$\prec_K$$ is defined as

$$x \prec_K y \implies y-x \in \textbf{int}\, K$$.