Polyhedral Geometry

Katta G. Murty ()
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Katta G. Murty: University of Michigan

Chapter Chapter 4 in Optimization for Decision Making, 2010, pp 167-233 from Springer

Abstract: Abstract A hyperplane in R n is the set of feasible solutions of a single linear equation. Let H = { x : a 1 x 1 + ⋯ + a n x n = a 0}, where the coefficient vector (a 1, …, a n )≠0, be a hyperplane in R n . Only when n = 2 (i.e., in R 2 only) every hyperplane is a straight line, and vice versa. In Fig. 4.1, we show the hyperplane (straight line in R 2) corresponding to the equation x 1 + x 2 = 1. When n ≥ 3, hyperplanes are not straight lines. Figure 4.2 shows a portion of the hyperplane corresponding to the equation x 1 + x 2 + x 3 = 1 in R 3.

Keywords: Feasible Solution; Extreme Point; Basic Vector; Inequality Constraint; Convex Polyhedron (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4419-1291-6_4

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