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In linear algebra, a power cone is a kind of a convex cone that is particularly important in modeling convex optimization problems. [1] It is a generalization of the quadratic cone: the quadratic cone is defined using a quadratic equation (with the power 2), whereas a power cone can be defined using any power, not necessarily 2.
The n-dimensional power cone is parameterized by a real number . It is defined as: [1]
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. [1]