Mathematical Developments Arising from Linear Programming

In recent years, there has been intense work in linear and nonlinear programming, much of it centered on understanding and extending the ideas underlying N. Karmarkar's interior-point linear programming algorithm, which was presented in 1984. This interdisciplinary research was the subject of an AMS Summer Research Conference on Mathematical Developments Arising from Linear Programming, held at Bowdoin College in the summer of 1988, which brought together researchers in mathematics, computer science, and operations research. This volume contains the proceedings from the conference. Among the topics covered in this book are: completely integrable dynamical systems arising in optimization problems, Riemannian geometry and interior-point linear programming methods, concepts of approximate solution of linear programs, average case analysis of the simplex method, and recent results in convex polytopes. Some of the papers extend interior-point methods to quadratic programming, the linear complementarity problem, convex programming, multi-criteria optimization, and integer programming. Other papers study the continuous trajectories underlying interior point methods. This book will be an excellent resource for those interested in the latest developments arising from Karmarkar's linear programming algorithm and in path-following methods for solving differential equations.