Abstract
An algorithm is developed for the problem of finding the point of smallest Euclidean norm in the convex hull of a given finite point set in a Euclidean space, with particular attention paid to the description of the procedure in geometric terms.
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References
E.W. Barankin and R. Dorfman, “Toward quadratic programming”, Rept. to the Logistics Branch, Office of Naval Research (January, 1955), unpublished.
E.W. Barankin and R. Dorfman, “On quadratic programming”, University of California Publications in Statistics 2 (1958) 285–318.
E.M.L. Beale, “Numerical methods”, Parts ii–iv, in: Nonlinear programming, Ed. J. Abadie (North-Holland, Amsterdam, 1967) pp. 143–172.
M.D. Canon and C.D. Cullum, “The determination of optimum separating hyperplans I. A finite step procedure”, RC 2023, IBM Watson Research Center, Yorktown Heights, N.Y. (February, 1968).
R.W. Cottle, “The principal pivoting method of quadratic programming”, in: Mathematics of the decision sciences, Part I, Vol. 11 of Lectures in Applied Mathematics, Eds. G.B. Dantzig and A.F. Veinott (A.M.S., Providence, R.I., 1968) pp. 144–162.
R.W. Cottle and G.B. Dantzig, “Complementary pivot theory”, in: Mathematics of the decision sciences, Part I, Vol. 11 of Lectures in Applied Mathematics, Eds. G.B. Dantzig and A.F. Veinott (A.M.S., Providence, R.I., 1968) pp. 115–136.
G.B. Dantzig, Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963).
G.B. Dantzig and A.F. Veinott, Eds., Mathematics of the decision sciences, Part I, Vol. 11 of Lectures in Applied Mathematics (A.M.S., Providence, R.I., 1968).
R. Fletcher, “A general quadratic programming algorithm”, T.P. 401, Theoretical Physics Div., U.K.A.E.A. Research Group, A.E.R.E., Harwell (March, 1970).
M. Frank and P. Wolfe, “An algorithm for quadratic programming”, Naval Research Logistics Quarterly 3 (1956) 95–110.
H.W. Kuhn and A.W. Tucker, “Nonlinear programming”, in: Proceedings of the second Berekeley symposium on mathematical statistics and probability, Ed. J. Neyman (University of California Press, Berkeley, Calif., 1951) pp. 481–492.
C.E. Lemke, “On complementary pivot theory” in: Mathematics of the decision sciences, Part I, Vol. 11 of Lectures in Applied Mathematics, Eds. G.B. Dantzig and A.F. Veinott (A.M.S. Providence, R.I., 1968) pp. 95–114.
T.D. Parsons and A.W. Tucker, “Hybrid programs: linear and least-distance”, Mathematical Programming 1 (1971) 153–167.
A.W. Tucker, “Analogues of Kirchoff’s laws”, Preprint LOGS 65, Stanford University Stanford, Calif. (July 1950).
A.W. Tucker, “On Kirchoff’s laws, potential, Lagrange multipliers, etc.”, NAML Rept. 52-17, National Bureau of Standards, Institute for Numerical Analysis, University of California, Los Angeles, Calif. (August, 1951).
A.W. Tucker, “Combinatorial theory underlying linear programs”, in: Recent advances in mathematical programming, Eds. R.L. Graves and P. Wolfe (McGraw-Hill, New York, 1963) pp. 1–16.
A.W. Tucker, “Principal pivot transforms of square matrices”, SIAM Review 5 (1963) 305.
A.W. Tucker, “A least-distance approach to quadratic programming”, in: Mathematics of the decision sciences, Part I, Vol. 11 of Lectures in Applied Mathematics. Eds. G.B. Dantzig and A.F. Veinott (A.M.S., Providence, R.I., 1968) pp. 163–176.
A.W. Tucker, “Least-distance programming”, in: Proceedings of the Princeton symposium on mathematical programming, Ed. H.W. Kuhn (Princeton University Press, Princeton, N. J., 1971) pp. 583–588.
P. Wolfe, “A simplex method for quadratic programming”, ONR Logistics Project Report., Princeton University, Princeton, N. J. (February 1957).
P. Wolfe, “The simplex method for quadratic programming”, Econometrica 27 (1959) 382–393.
P. Wolfe, “Finding the nearest point in a polytope”, RC 4887, IBM Research Center, Yorktown Heights, N.Y. (June, 1974).
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© 1974 The Mathematical Programming Society
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Wolfe, P. (1974). Algorithm for a least-distance programming problem. In: Balinski, M.L. (eds) Pivoting and Extension. Mathematical Programming Studies, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121249
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DOI: https://doi.org/10.1007/BFb0121249
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