The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."

Most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear programming were presented. The common feature to most of the new polynomial algorithms is the path-following aspect. The method of McCormick-Sofer for convex programming also follows a path. Efforts in the theoretical analysis of algorithms was also reported. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference it was still not clear weather the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms. In other presentations, Fourer-Gay-Kernighan presented a programming language (AMPL) for mathematical programming, David Gay presented graphic illustrations of the performance of Karmarkar's algorithm, and James Ho discussed embedding of linear programming in commonly used spreadsheets.

This book is concerned with theoretical developments in the area of mathematical programming including new algorithms (analytic and heuristic) and their applications in science and industry. It exposes recent mathematical developments to a larger audience in science and industry who may not be equipped with the necessary research background and provides good references in many branches of mathematical programming. The text includes research and tutorial papers giving details of use of recent developments in applied areas, as well as review and state-of-the-art papers providing a soruce of references to researchers in this field.

Setting out to bridge the gap between the theory of mathematical programming and the varied, real-world practices of industrial engineers, this work introduces developments in linear, integer, multiobjective, stochastic, network and dynamic programing. It details many relevant industrial-engineering applications.;College or university bookstores may order five or more copies at a special student price, available upon request from Marcel Dekker, Inc.

The historical span of mathematical programming, from its conception to its present flourishing state is remarkably short. The 1940's and 1950's were an exciting period when there was a great deal of research activity, but the growth of the field during the 1960's and 1970's worldwide already appears to be of historical interest too, because much of the progress during that time has had an important influence on present-day research. In this volume some pioneers of the field, as well as some prominent younger colleagues, have put their personal recollections in writing. The contributions bear witness to a time of impressive scientific progress, in which the rich new field of mathematical programming was detected and brought up.

This work is concerned with theoretical developments in the area of mathematical programming, development of new algorithms and software and their applications in science and industry. It aims to expose recent mathematical developments to a larger audience in science and industry.

Mathematical Programming provides information pertinent to the developments in mathematical programming. This book covers a variety of topics, including integer programming, dynamic programming, game theory, nonlinear programming, and combinatorial equivalence. Organized into nine chapters, this book begins with an overview of optimization of very large-scale planning problems that can be achieved on significant problems. This text then introduces non-stationary policies and determines certain operating characteristics of the optimal policy for a very long planning horizon. Other chapters consider the perfect graph theorem by defining some well-known integer-valued functions of an arbitrary graph. This book discusses as well integer programming that deals with the class of mathematical programming problems in which some or all of the variables are required to be integers. The final chapter deals with the basic theorem of game theory. This book is a valuable resource for readers who are interested in mathematical programming. Mathematicians will also find this book useful.