ILOG CPLEX 11.0 User's Manual

Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(-1, -1)Figure 13.2 x 2 + y 2 ≥ 1 is not convexIt might be less obvious at first glance that the equality x 2 + y 2 = 1 is not convex either. Asyou see in Figure 13.3, there may be a continuous line segment that joins two arbitrarypoints, such as e and f, in the domain but the line segment may pass outside the domain.Another way to see this idea is to note that an equality constraint is algebraically equivalentto the intersection of two inequality constraints of opposite sense, and you have already seenthat at least one of those quadratic inequalities will not be convex. Thus, the equality is notconvex either.ILOG CPLEX 11.0 — USER’ S MANUAL 241