Could somebody what $\mathbb{K}$ signifies in the function definition ? If it was $\mathbb{R}$ it could mean Real space
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$\mathbb K$ is apparently a field over which we have an inner product space; e.g., $\mathbb K=\mathbb R$ or $\mathbb C$ – J. W. Tanner Jun 07 '20 at 11:35
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@J.W.Tanner I don't think that it can be $\mathbb C$ because in the definition of the half-space you need an ordered field. And $\mathbb C$ can't be ordered. – mathcounterexamples.net Jun 07 '20 at 11:41
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@mathcounterexamples.net: I see what you mean – J. W. Tanner Jun 07 '20 at 11:43
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1@spaul Where is his coming from? Because I think that there is a mistake in the half-space definition. It shouldn't be $\vec{a}.\vec{x} \le \vec{b}$ but $\vec{a}.\vec{x} \le b$ where $b \in \mathbb K$. – mathcounterexamples.net Jun 07 '20 at 11:44
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https://web.cse.ohio-state.edu/~pouchet.2/lectures/doc/888.11.1.pdf – spaul Jun 07 '20 at 12:02
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From the given link. Introduction to polyhedral model – spaul Jun 07 '20 at 12:03
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@mathcounterexamples.net From the given link. Introduction to polyhedral model – spaul Jun 07 '20 at 13:45