# Projection on Polyhedral Cone

### From Wikimization

(→external links) |
|||

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:// | + | [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.

You are welcome and encouraged to write your thoughts about this problem here.

### external links

More about projection on cones (and convex sets, more generally) can be found here (chapter E):

http://meboo.convexoptimization.com/Meboo.html

More about polyhedral cones can be found in chapter 2.