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Mathematical Developments Arising from Linear Programming

About this Title

Jeffrey C. Lagarias and Michael J. Todd, Editors

Publication: Contemporary Mathematics
Publication Year: 1990; Volume 114
ISBNs: 978-0-8218-5121-0 (print); 978-0-8218-7702-9 (online)
DOI: https://doi.org/10.1090/conm/114
MathSciNet review: 1097861

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Table of Contents

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Front/Back Matter

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1. Recent Progress and New Directions

• Carl W. Lee – Some recent results on convex polytopes [MR 1097862]
• Karl-Heinz Borgwardt – Probabilistic analysis of the simplex method [MR 1097863]
• Nimrod Megiddo – On solving the linear programming problem approximately [MR 1097864]
• Narendra Karmarkar – Riemannian geometry underlying interior-point methods for linear programming [MR 1097865]
• A. M. Bloch – Steepest descent, linear programming, and Hamiltonian flows [MR 1097866]

2. Interior-Point Methods for Linear Programming

• Yinyu Ye – An $O(n^3L)$ potential reduction algorithm for linear programming [MR 1097867]
• R. J. Vanderbei and J. C. Lagarias – I. I. Dikin’s convergence result for the affine-scaling algorithm [MR 1097868]
• Irvin J. Lustig – Phase $1$ search directions for a primal-dual interior point method for linear programming [MR 1097869]
• Earl R. Barnes – Some results concerning convergence of the affine scaling algorithm [MR 1097870]
• Kurt M. Anstreicher – Dual ellipsoids and degeneracy in the projective algorithm for linear programming [MR 1097871]
• Miroslav D. Ašić, Vera V. Kovačević-Vujčić and Mirjana D. Radosavljević-Nikolić – A note on limiting behavior of the projective and the affine rescaling algorithms [MR 1097872]

3. Trajectories of Interior-Point Methods

• Christoph Witzgall, Paul T. Boggs and Paul D. Domich – On the convergence behavior of trajectories for linear programming [MR 1097873]
• Ilan Adler and Renato D. C. Monteiro – Limiting behavior of the affine scaling continuous trajectories for linear programming problems [MR 1097874]
• Renato D. C. Monteiro – Convergence and boundary behavior of the projective scaling trajectories for linear programming [MR 1097875]

4. Nonlinear Optimization

• F. Jarre, G. Sonnevend and J. Stoer – On the complexity of a numerical algorithm for solving generalized convex quadratic programs by following a central path [MR 1097876]
• Bahman Kalantari – Canonical problems for quadratic programming and projective methods for their solution [MR 1097877]
• Sanjay Mehrotra and Jie Sun – An interior point algorithm for solving smooth convex programs based on Newton’s method [MR 1097878]
• A. A. Goldstein – A modified Kantorovich inequality for the convergence of Newton’s method [MR 1097879]

5. Integer Programming and Multi-Objective Programming

• Narendra Karmarkar – An interior-point approach to NP-complete problems. I [MR 1097880]
• John E. Mitchell and Michael J. Todd – Solving matching problems using Karmarkar’s algorithm [MR 1097881]
• S. S. Abhyankar, T. L. Morin and T. Trafalis – Efficient faces of polytopes: interior point algorithms, parameterization of algebraic varieties, and multiple objective optimization [MR 1097882]