Talk:Projection on Polyhedral Cone

From Wikimization

Revision as of 04:51, 9 June 2008 by 72.141.247.157 (Talk)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Jump to: navigation, search

The definition of projection should be made clear. If, by projection you mean the nearest point to the cone, then this results in a quadratic programming problem, i.e. given the point LaTeX: \bar x and the cone LaTeX: K=\left\{x: Ax \leq b \right\}, then the quadratic program is LaTeX: \begin{array}{rcl} \min & \|x-\bar x\|^2_2 \\ \mbox{s.t.} & x \in K \end{array}

No explicit formula for a solution of a quadratic program exists (or for the solution of a linear program). It is doubtful that such a formula will be found due to the combinatorial nature of the problem.

Retrieved from "http://www.convexoptimization.com/wikimization/index.php/Talk:Projection_on_Polyhedral_Cone"
Personal tools