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The simplex method / K.H. Borgwardt (1987)
Titre : The simplex method : Aprobabilistic analysis Type de document : Monographie Auteurs : K.H. Borgwardt, Auteur Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 1987 Importance : 268 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-0-387-17096-1 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques
[Termes IGN] algorithme du simplexe
[Termes IGN] asymptote
[Termes IGN] estimation statistique
[Termes IGN] modèle stochastique
[Termes IGN] optimisation (mathématiques)
[Termes IGN] Ploynôme
[Termes IGN] probabilitésNote de contenu : 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 Hairnovich
8 Quadratic expected number of steps for signinvariance model
Discussion of different stochastic models
9 What is the "Real World Model” ?
Outline of Chapters 15
10 The basic ideas and the methods of this book
11 The results of this book
12 Conclusion and conjectures
1 THE SHADOWVERTEX 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 SimplexMethod
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 boundarycondition
4 Explicit formulation of the intersectioncondition
5 Componentwise signindependence and the intersection condition
6 The average number of pivot steps
6 APPENDIX
1 Gammafunction and Betafunction
2 Unit ball and unit sphere
3 Estimations under variation of the weightsNuméro de notice : 68115 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=61864 Réservation
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