Boolean Methods in Operations Research and Related Areas

Abstract

In classical analysis, there is a vast difference between the class of problems that may be handled by means of the methods of calculus and the class of problems requiring combinatorial techniques. With the advent of the digital computer, the distinction begins to blur, and with the increasing emphasis on problems involving optimization over structures, tIlE' distinction vanishes. What is necessary for the analytic and computational treatment of significant questions arising in modern control theory, mathematical economics, scheduling theory, operations research, bioengineering, and so forth is a new and more flexible mathematical theory which subsumes both the cla8sical continuous and discrete t 19orithms. The work by HAMMER (IVANESCU) and RUDEANU on Boolean methods represents an important step in this dnectlOn, and it is thus a great pleasure to welcome it into print. It will certainly stimulate a great deal of additional research in both theory and application. RICHARD BELLMAN University of Southern California * With the exception of § § 1-4 in eh. III and of § § 1-2 in eh. V. Mrs. ANNm B.~LESCU. To all of them we expreRs onr deep gratituc\r August 1967. PETER L HAMMER (IVANESCU). SERGIU RUDEANU

Reformulations in Mathematical Programming: Definitions and Systematics

“…Binary Quadratic Programs (BQP) have attracted a considerable amount of attentions, mostly because of the fact that there is an easy exact linearization [22] that presents some practical drawbacks. Extensive work was carried out by research teams led by A. Billionnet [13], F. Glover [1], P. Hammer [35], P. Hansen [36] (see Sect. 4.1), Ph.…”

Une méthode de résolution des programmes non-linéaire partiellement discrets sans hypothèse de convexité

“…Le théorème de Gaspar affirme d'ailleurs que toute fonction de variables bivalentes s'exprime par un polynôme par rapport à ces mêmes variables. Pour un procédé constructif, voir Hammer et Rudeanu, 1968 (Part 1, § 1). …”

“…Il y a même mieux encore, puisque tout programme totalement bivalent est équivalent à un programme linéaire du même type (Hammer et Rudeanu, 1968; le lecteur pourra éclaircir ce point en notant que l'enveloppe convexe d'un ensemble de sommets du cube unité ne contient aucun autre sommet de ce cube).…”

Approximation Algorithms for Discrete Polynomial Optimization

“…As such it has received attention in the literature; see [17,18]. It is also known as Fourier support graph problem.…”