# Convex cones

### From Wikimization

## Nonorthogonal projection on extreme directons of convex cone

### pseudo coordinates

Let be a full-dimensional closed pointed convex cone in finite-dimensional Euclidean space .

For any vector and a point , define to be the largest number such that .

Suppose and are points in .

Further, suppose that for every extreme direction of .

Then must be equal to .

### proof

is the optimal value of a conic program: