If two extreme points are optimal, then so is every point on the line segment connecting the two extreme points.

Question

Quizplus · Accepted Answer

This is true for convex optimization problems. Since the line segment between two extreme points lies entirely within the convex set of feasible solutions, any point on that line segment is also a feasible solution. If both extreme points are optimal, then any convex combination of them (i.e. any point on the line segment) is also optimal.

If Two Extreme Points Are Optimal, Then So Is Every