Affine hull vs. convex hull

The affine hull and convex hull are closely related concepts. Let be a set in . The affine hull of is the set of all affine combinations of elements of : The convex hull of is the set of all convex combinations of the elements of : Putting the definitions side by side, we see […]

Affine hull vs. convex hull

The Lagrange dual function is always concave

Consider an optimization problem in standard form: with the variable . Let be the domain for , i.e. the intersection of the domains of the ‘s and the ‘s. The Lagrangian associated with this problem is the function defined as with domain . The Lagrange dual function is the function defined as the minimum value […]

The Lagrange dual function is always concave