Geodesic
Projection onto polyhedra in outer representation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 387-396

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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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     author = {E. A. Nurminski},
     title = {Projection onto polyhedra in outer representation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {387--396},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a3/}
}
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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/