Advances in computer technology have pointed out the next important area of computer applications: solution of non-numerical problems. It is hardly necessary to emphasize the importance of these kind of problems. First of all most of the decisions one has to make in real-life situations are non-numerical in the first instance and can be represented as numerical problems only as approximations which are often only partially valid. Second, to use the computer to its full potential it should be employed as a logical machine, capable of deduction, and not just as a numerical calculating machine....

These notes are based on the material presented in a series of lec tures in the IBM Systems Research Institute (ESRI) in Geneva durJng 1967-1969 to systems engineers working in the design and programming of computer systems for control and monitoring of i nustrial proc esses. The purpose of the lectures and this book is to give a survey of dif ferent approaches in developing models to describe the behavior of the process in terms of controllable variables. It does not cover the theory of control, stability of control systems, nor techniques in data acquisition or problems in instrumentation...

The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining...

1 In an artic1e in the Review of Economic Studies, G1ustoff attempts to prove the existence of a Keynesian "equilibrium". The significance of his article tran- scends its explicit purpose of proving existence, since it deals with the more fun- damental question of what is the nature of a Keynesian equilibrium with involuntary unemp1pymant: Moreover, it approaches the problem frPlIl an unorthodox point of view. 4 G1ustoff follows the direction of C1ower,3 who in turn goes back to Morishima and Patinkin;5 that is, unlike the theory based on ex ante demand or supply functions, he redefines the...

This volume on the proceedings of a symposium on Resource Allocation and Division of Space represents a revised interest in the old problem of allocation and a fresh attack on the increasingly vital problem of space management. The symposium was held at the Toba International Hotel, near Nagoya, Japan in December, 1975. Although the contributions included in this volume are all broadly concerned with either resource allocation or spatial problems, the editors have selected papers essentially on the basis of scientific merits and orginality rather than on the basis of narrowly focused topics...

Economic theory is growing not only in depth but in the breadth of its application as well. This study encroaches in part on a field normally considered as the domain of Sociology. But the methods applied here are those of mathematical economics. It has not been my ambition to make this as general and as mathe matically demanding as possible. On the contrary, I wanted to present as simple an argument as possible throughout. I wish to thank Brown University for granting me a Sabbatical leave in the Fall of 1977-78 in the course of which I wrote the first draft of this monograph. I am also...

During the fifties and the sixties the neoclassical concept of the production function was criticized in numerous papers. In particular, the aggregation of different capital goods into a single number was reprehended. A second essential disadvantage, namely the neglect of the time structure of the production process, found, however, rela tively little attention. While up to the thirties the Austrian capital theory which stressed the time aspect of production was an important school, it fell into oblivion after the great capital controversies of the thirties. It took over thirty years, i. e....

On February 20, 1978, the Department of Econometrics of the University of Tilburg organized a symposium on Convex Analysis and Mathematical th Economics to commemorate the 50 anniversary of the University. The general theme of the anniversary celebration was "innovation" and since an important part of the departments' theoretical work is con centrated on mathematical economics, the above mentioned theme was chosen. The scientific part of the Symposium consisted of four lectures, three of them are included in an adapted form in this volume, the fourth lec ture was a mathematical one with the...

This book has grown out of a desire to explore the possibilities of using optimizing models in transportation planning. This approach has been followed throughout. Models which combine descriptive and optimizing elements are not treated. The gravity model is here studied as the solution to an optimizing model. In spite of this approach, much of the material shoula be of general interest. Algorithms are not discussed. The author has benefited from discussions with many colleagues. M. Florian suggested the term "interacti vi ty." N. F. Stewart and P. Smeds gave many valu able comments on a...