×
Wolfe, Philip

Finding the nearest point in a polytope. (English) Zbl 0352.90046

Math. Program. 11, 128-149 (1976).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0352.90046

Cited in 3 Reviews
Cited in 126 Documents

MSC:

90C20 Quadratic programming
90C30 Nonlinear programming
90C25 Convex programming
52Bxx Polytopes and polyhedra
PDF BibTeX XML Cite
\textit{P. Wolfe}, Math. Program. 11, 128--149 (1976; Zbl 0352.90046)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] R.O. Barr, ”An efficient computational procedure for a generalized quadratic programming problem”,SIAM Journal on Control 7 (1969) 415–429. · Zbl 0182.20701
[2] L.C. Barbosa and E. Wong, ”On a class of iterative algorithms for linear inequalities with applications to pattern classification”, in:Proceedings of the first annual Princeton conference of information sciences and systems, 1967, pp. 86–89.
[3] M.D. Canon and C.D. Cullum, ”The determination of optimum separating hyperplanes I. A finite step procedure”, RC 2023, IBM Watson Research Center, Yorktown Heights, New York (February, 1968). · Zbl 0186.24002
[4] G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J. 1963).
[5] E.G. Gilbert, ”An iterative procedure for computing the minimum of a quadratic form on a convex set”,SIAM Journal on Control 4 (1966) 61–80. · Zbl 0196.51204
[6] G.H. Golub and M.A. Saunders, Linear least squares and quadratic programming, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970) Ch. 10. · Zbl 0334.90034
[7] B. von Hohenbalken, ”A finite algorithm to maximize certain pseudoconcave functions on polytopes”,Mathematical Programming 9 (1975) 189–206. · Zbl 0323.90042
[8] O.L. Mangasarian, ”Linear and nonlinear separation of patterns by linear programming”,Operations Research 13 (1965) 444–452. · Zbl 0127.36701
[9] B.F. Mitchell, V.F. Demyanov, and V.N. Malozemov, ”Finding the point of a polyhedron closest to the origin”,SIAM Journal on Control 12 (1974) 19–26. · Zbl 0277.52007
[10] J. Stoer and C. Witzgall,Convexity and optimization in finite dimensions I (Springer, Berlin, 1970). · Zbl 0203.52203
[11] D.R. Wilhelmsen, A linear algorithm for generating positive weight cubatures,Mathematics of Computation 30 (1976) to appear. · Zbl 0326.65024
[12] C. Witzgall, correspondence with P. Wolfe (December, 1974).
[13] P. Wolfe, ”Convergence theory in nonlinear programming”, in: J. Abadie, ed.,Integer and nonlinear programming, (North-Holland, Amsterdam, 1970) pp. 1–36. · Zbl 0336.90045
[14] P. Wolfe, ”Algorithm for a least-distance programming problem”,Mathematical Programming Study 1 (1974) 190–205. · Zbl 0359.90062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.