Abstract
Our goal is to give an exposition of our work on the average speed of the simplex method. Detailed proofs are in Smale 1982. Here we concentrate on the main ideas, with concepts emphasized. Some new things are added.
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References
Balinski, M. and Cottle, R., Complementarity and Fixed Point Problems, North-Holland, Amsterdam, 1978.
Borgwardt, K., The Average Number of Pivot Steps Required by the Simplex-Method is Polynomial, preprint.
Cottle, R. and Dantzig, G., 1968, Complementary Pivot Theory of Mathematical Programming, in Math, of the Decision Sciences (G. Dantzig and A. Veinott, Jr., eds.) Amer. Math. Soc. Providence, R I., pp. 115–136.
Dantzig, G., 1963, Linear Programming and Extensions, Princeton Univ. Press, Princeton, N.J.
Eaves, C. and Scarf, H., 1976, The Solution of Systems of Piecewise Linear Equations, Math. Operations Res. Vol. 1, pp. 1–27.
Hadley, G., 1962, Linear Programming, Addison-Wesley, Reading, Mass.
Hirsch, M. and Smale, S., 1979, On Algorithms for Solving f(x) = 0. Commun. Pure. Appl. Math. 32. pp. 281–312.
Klee, V. and Minty, G., 1972, How Good is the Simplex Algorithm? in O. Shisha, ed.: Inequalities III, Academic Press, New York, pp. 159–175.
Lovász, L., 1980, A New Linear Programming Algorithm-Better or Worse Than the Simplex Method?, The Mathematical Intelligencer, vol. 2, pp. 141–146.
Shub, M. and Smale, S., 1982, Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: Part I. Preprint.
Smale, S., 1976, A Convergent Process of Price Adjustment and Global Newton Methods, J. Math. Economics, 3, pp. 107–120.
Smale, S., 1981, The Fundamental Theorem of Algebra and Complexity Theory, Bull. Amer. Math. Soc., vol. 4, pp. 1–36.
Smale, S., 1982, On the Average Speed of the Simplex Method of Linear Programming, preprint (submitted to “Mathematical Programming”).
Traub, J. and Wozniakowski, H., 1982, Complexity of Linear Programming, Operations Research Letters, vol. 1, pp. 59–62.
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© 1983 Springer-Verlag Berlin Heidelberg
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Smale, S. (1983). The Problem of the Average Speed of the Simplex Method. In: Bachem, A., Korte, B., Grötschel, M. (eds) Mathematical Programming The State of the Art. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68874-4_20
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DOI: https://doi.org/10.1007/978-3-642-68874-4_20
Publisher Name: Springer, Berlin, Heidelberg
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