Chapter 11 Linear Programming

This lecture is about a special type of optimization problems, namely linear programs. We start with a geometric problem that can directly be formulated as a linear program. Let P ⊆ R d and Q ⊆ R d be two finite point sets in d-dimensional space. We want to know whether there exists a hyperplane that separates P from Q (we allow non-strict separation, i.e. some points are allowed to be on the hyperplane). Figure 11.1 illustrates the 2-dimensional case. Figure 11.1: Left: there is a separating hyperplane; Right: there is no separating hyperplane How can we formalize this problem? A hyperplane is a set of the form