Geodesic
Finding the projection of a given point on the set of solutions of a linear programming problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 33-47 
A. I. Golikov; Yu. G. Evtushenko. Finding the projection of a given point on the set of solutions of a linear programming problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 33-47. http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a4/
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     title = {Finding the projection of a~given point on the set of solutions of a~linear programming problem},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The problem of finding the projections of points on the sets of solutions of primal and dual problems of linear programming is considered. This problem is reduced to a single solution of the problem of minimizing a new auxiliary function, starting from some threshold value of the penalty coefficient. Estimates of the threshold value are obtained. A software implementation of the proposed method is compared with some known commercial and research software packages for solving linear programming problems.

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