A big-M type method for the computation of projections onto polyhedrons. (English) Zbl 0552.90076
In a previous work [ibid. 43, 495-525 (1984; Zbl 0518.65044)], we examined some active constraints methods for the computation of the projection of a point onto a polyhedron when a feasible point is known. In this paper, we assume that such a point is not known and examine a method similar to the big-M method developed for the solution of linear programming problems. Special attention is given to the study of computing error propagation.
MSC:
| 90C30 | Nonlinear programming |
| 65K05 | Numerical mathematical programming methods |
| 49M37 | Numerical methods based on nonlinear programming |
Keywords:
active constraints methods; big-M method; error propagation; projection onto polyhedra; active set methods; orthogonal factorizationReferences:
| [1] | Arioli, M., Laratta, A., andMenchi, O.,Numeric Computation of the Projection of a Point onto a Polyhedron, Journal of Optimization Theory and Applications, Vol. 43, pp. 495-525, 1984. · Zbl 0518.65044 · doi:10.1007/BF00935003 |
| [2] | Zoutendijk, G.,Mathematical Programming Methods, North-Holland, Amsterdam, Holland, 1976. · Zbl 0337.90036 |
| [3] | Arioli, M., andLaratta, A., Metodi Diretti per la Risoluzione di Sistemi Lineari, Calcolo, Vol. 21, pp. 229-252, 1984. · Zbl 0574.65032 · doi:10.1007/BF02576535 |
| [4] | Arioli, M., andLaratta, A.,Error Analysis of an Algorithm for Solving an Underdetermined System, Numerische Mathematik (to appear). · Zbl 0543.65012 |
| [5] | Kinderleher, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980. |
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