Geodesic
Projection onto polyhedra in outer representation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 387-396 
E. A. Nurminski. Projection onto polyhedra in outer representation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 387-396. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a3/
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     author = {E. A. Nurminski},
     title = {Projection onto polyhedra in outer representation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The projection of the origin onto an $n$-dimensional polyhedron defined by a system of $m$ inequalities is reduced to a sequence of projection problems onto a one-parameter family of shifts of a polyhedron with at most $m+1$ vertices in $n+1$ dimensions. The problem under study is transformed into the projection onto a convex polyhedral cone with m extreme rays, which considerably simplifies the solution to an equivalent problem and reduces it to a single projection operation. Numerical results obtained for random polyhedra of high dimensions are presented.

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