Convex Polygons & Properties

Version 12 adds convex optimization and opens up many applications in classes of problems that can be identified to be convex in geometry.

Find the inequality representation for a convex polygon using LinearOptimization.

The analytic center of a convex polygon can be defined as a point inside the polygon that maximizes the product of distances to the sides. The distance of a point in the polygon to each side is , and so the analytic center is that maximizes . To express the problem as a convex minimization, take and negate the objective . The transformed objective is .

Visualize the location of the analytic center.