
Geometry of Linear Programming 49
FIGURE 2.7
Convexity and non-convexity.
2.2.1 Geometry of Optimal Solutions
In this section we develop a geometric characterization of optimal solutions for
linear programs based on insights from low dimensional problems. Consider
the linear program (2.1). The objective function is −x
1
−2x
2
= c
T
x. Consider
contours of the objective function H =