Convex cones
From Wikimization
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+ | <math>\,d_v(x)\,</math> is the optimal value of a conic program: | ||
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+ | <math>\,\begin{array}{rl}\mathrm{maximize}&t\\ | ||
+ | \mathrm{subject~to}&x-t^{}v\in\mathcal{K}\end{array}</math> |
Revision as of 21:02, 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: