Electronic Design Automation

4.5.4. Convex optimization problem

As mentioned in Subsection 4.5.1, the constraints in the convex optimization problem are convex functions with the following convexity property (Figure 4.31):where α ≥ 0, β ≥ 0, and α + β = 1. Conceptually, the convexity property can be illustrated as follows:

FIGURE 4.31. The convexity property.

In other words, given two points x^a and x^b from the set of points defined by a convex function, all the points on the line segment between x^a and x^b will also belong to the set (i.e., the dash region), which is called ...