# Convex cones

### From Wikimization

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===proof=== | ===proof=== | ||

+ | <math>\,d_v(x)\,</math> is the optimal value of a conic program: | ||

+ | |||

+ | <math>\,\begin{array}{rl}\mathrm{maximize}&t\\ | ||

+ | \mathrm{subject~to}&x-t^{}v\in\mathcal{K}\end{array}</math> |

## Revision as of 20:02, 28 August 2008

## 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: