# Projection on Polyhedral Cone

(Difference between revisions)
 Revision as of 17:22, 27 February 2009 (edit)← Previous diff Revision as of 17:00, 15 April 2009 (edit) (undo) (→external links)Next diff → Line 16: Line 16: More about projection on cones (and convex sets, more generally) can be found here (chapter E): More about projection on cones (and convex sets, more generally) can be found here (chapter E): - [http://www.convexoptimization.com/TOOLS/0976401304.pdf http://www.convexoptimization.com/TOOLS/0976401304.pdf] + [http://meboo.convexoptimization.com/Meboo.html http://meboo.convexoptimization.com/Meboo.html] More about polyhedral cones can be found in chapter 2. More about polyhedral cones can be found in chapter 2.

## Revision as of 17:00, 15 April 2009

This is an open problem in Convex Optimization. At first glance, it seems rather simple; the problem is certainly easily understood:

We simply want a formula for projecting a given point in Euclidean space on a cone described by the intersection of an arbitrary number of halfspaces;
we want the closest point in the polyhedral cone.

By "formula" I mean a closed form; an equation or set of equations (not a program, algorithm, or optimization).
A set of formulae, the choice of which is conditional, is OK as long as size of the set is not factorial (prohibitively large).

This problem has many practical and theoretical applications. Its solution is certainly worth a Ph.D. thesis in any Math or Engineering Department.