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Micheal J Todd

Bio: Micheal J Todd is an academic researcher from Cornell University. The author has contributed to research in topics: Simplex algorithm & Lemke's algorithm. The author has an hindex of 1, co-authored 1 publications receiving 83 citations.

Papers
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Journal ArticleDOI
TL;DR: It is shown that a particular pivoting algorithm, which is called the lexicographic Lemke algorithm, takes an expected number of steps that is bounded by a quadratic inn, when applied to a random linear complementarity problem of dimensionn.
Abstract: We show that a particular pivoting algorithm, which we call the lexicographic Lemke algorithm, takes an expected number of steps that is bounded by a quadratic inn, when applied to a random linear complementarity problem of dimensionn. We present two probabilistic models, both requiring some nondegeneracy and sign-invariance properties. The second distribution is concerned with linear complementarity problems that arise from linear programming. In this case we give bounds that are quadratic in the smaller of the two dimensions of the linear programming problem, and independent of the larger. Similar results have been obtained by Adler and Megiddo.

85 citations


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Book
01 Jan 1996
TL;DR: The Simplex Method in Matrix Notation and Duality Theory, and Applications: Foundations of Convex Programming.
Abstract: Preface. Part 1: Basic Theory - The Simplex Method and Duality. 1. Introduction. 2. The Simplex Method. 3. Degeneracy. 4. Efficiency of the Simplex Method. 5. Duality Theory. 6. The Simplex Method in Matrix Notation. 7. Sensitivity and Parametric Analyses. 8. Implementation Issues. 9. Problems in General Form. 10. Convex Analysis. 11. Game Theory. 12. Regression. Part 2: Network-Type Problems. 13. Network Flow Problems. 14. Applications. 15. Structural Optimization. Part 3: Interior-Point Methods. 16. The Central Path. 17. A Path-Following Method. 18. The KKT System. 19. Implementation Issues. 20. The Affine-Scaling Method. 21. The Homogeneous Self-Dual Method. Part 4: Extensions. 22. Integer Programming. 23. Quadratic Programming. 24. Convex Programming. Appendix A: Source Listings. Answers to Selected Exercises. Bibliography. Index.

1,194 citations

BookDOI
01 Jan 1990

1,149 citations

Book
01 Jan 1987
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
Abstract: From the Publisher: Introduction to Numerical Continuation Methods continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business looking for an introduction to computational methods for solving a large variety of nonlinear systems of equations. A background in elementary analysis and linear algebra is adequate preparation for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

889 citations

Journal ArticleDOI
David S. Johnson1
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.

857 citations

Journal ArticleDOI
TL;DR: The smoothed analysis of algorithms is introduced, which continuously interpolates between the worst-case and average-case analyses of algorithms, and it is shown that the simplex algorithm has smoothed complexity polynomial in the input size and the standard deviation of Gaussian perturbations.
Abstract: We introduce the smoothed analysis of algorithms, which continuously interpolates between the worst-case and average-case analyses of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex algorithm has smoothed complexity polynomial in the input size and the standard deviation of Gaussian perturbations.

802 citations