2.8. Recall that for a two-dimensional problem, the Nelder–Mead algorithm maintains at each iteration a set of three possible solutions defining the vertices of a simplex, specifically a triangle. Let us consider whether three is a good choice. Imagine an algorithm for two-dimensional optimization that maintains four points defining the vertices of a convex quadrilateral and is similar to Nelder–Mead in spirit. Speculate how such a procedure could proceed. Consider sketches like those shown in Figure 2.10. What are some of the inherent challenges? There is no correct answer here; the purpose is to brainstorm and see where your ideas lead.