Power cone


In linear algebra, a power cone is a kind of a convex cone that is particularly important in modeling convex optimization problems. It is a generalization of the quadratic cone: the quadratic cone is defined using a quadratic equation, whereas a power cone can be defined using any power, not necessarily 2.

Definition

The n-dimensional power cone is parameterized by a real number. It is defined as:

An alternative definition is

Applications

The main application of the power cone is in constraints of convex optimization programs. There are many problems that can be described as minimizing a convex function over a power cone.