Projection on Polyhedral Cone
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This is an open problem in Convex Optimization. At first glance, it seems rather simple; the problem is certainly easily understood: | 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 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 cone. |
This problem has many practical and theoretical applications. | This problem has many practical and theoretical applications. | ||
Revision as of 13:51, 9 June 2008
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 cone.
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.