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The Simplex Method

A Probabilistic Analysis
BuchKartoniert, Paperback
270 Seiten
Englisch
Springererschienen am01.11.1986
While the "worst-case analysis" of some variants of the method shows that this is not a "good" algorithm in the usual sense of complexity theory, it seems to be useful to apply other criteria for a judgement concerning the quality of the algorithm.mehr
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BuchKartoniert, Paperback
EUR53,49
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Produkt

KlappentextWhile the "worst-case analysis" of some variants of the method shows that this is not a "good" algorithm in the usual sense of complexity theory, it seems to be useful to apply other criteria for a judgement concerning the quality of the algorithm.
Details
ISBN/GTIN978-3-540-17096-9
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr1986
Erscheinungsdatum01.11.1986
ReiheAlgorithms and Combinatorics
Seiten270 Seiten
SpracheEnglisch
Gewicht433 g
IllustrationenXII, 270 p. 3 illus.
Artikel-Nr.10738453

Inhalt/Kritik

Inhaltsverzeichnis
0 Introduction.- Formulation of the problem and basic notation.- 1 The problem.- A Historical Overview.- 2 The gap between worst case and practical experience.- 3 Alternative algorithms.- 4 Results of stochastic geometry.- 5 The results of the author.- 6 The work of Smale.- 7 The paper of Haimovich.- 8 Quadratic expected number of steps for sign-invariance model.- Discussion of different stochastic models.- 9 What is the Real World Model ?.- Outline of Chapters 1-5.- 10 The basic ideas and the methods of this book.- 11 The results of this book.- 12 Conclusion and conjectures.- 1 The Shadow-Vertex Algorithm.- 1 Primal interpretation.- 2 Dual interpretation.- 3 Numerical realization of the algorithm.- 4 The algorithm for Phase I.- 2 The Average Number of Pivot Steps.- 1 The probability space.- 2 An integral formula for the expected number of S.- 3 A transformation of coordinates.- 4 Generalizations.- 3 The Polynomiality of the Expected Number of Steps.- 1 Comparison of two integrals.- 2 An application of Cavalieri´s Principle.- 3 The influence of the distribution.- 4 Evaluation of the quotient.- 5 The average number of steps in our complete Simplex-Method.- 4 Asymptotic Results.- 1 An asymptotic upper bound in integral form.- 2 Asymptotic results for certain classes of distributions.- 3 Special distributions with bounded support.- 4 Asymptotic bounds under uniform distributions.- 5 Asymptotic bounds under Gaussian distribution.- 5 Problems with Nonnegativity Constraints.- 1 The geometry.- 2 The complete solution method.- 3 A simplification of the boundary-condition.- 4 Explicit formulation of the intersection-condition.- 5 Componentwise sign-independence and the intersection condition.- 6 The average number of pivot steps.- 6 Appendix.- 1 Gammafunction andBetafunction.- 2 Unit ball and unit sphere.- 3 Estimations under variation of the weights.- References.mehr