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Power cone

From Wikipedia, the free encyclopedia

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.

Definition

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The n-dimensional power cone is parameterized by a real number . It is defined as:[1]

Applications

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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]

References

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  1. ^ a b c "MOSEK Modeling Cookbook - the Power Cones".