A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.     

Flintlock brass fittings from the 19th-century Akko 1 shipwreck,Israel

The Akko 1 shipwreck is the remains of a 26-metre-long Egyptian armed vessel or auxiliary naval brig built at the beginning of the 19th century. Remains of six flintlock muskets were retrieved from the shipwreck, and characterised by various metallurgical methods. The research aimed to study the composition and microstructure of the musket fittings and their manufacturing processes, and if possible, to determine the date and origin of the raw materials. The lead isotope analysis of the fittings suggests that their raw material originated in Great Britain. Based on their typology and composition, the fittings were made in Great Britain of brass alloy and manufactured by casting, probably at the same workshop; and the staple was manufactured by casting and drawing. Considering the zinc content, combined with the manufacturing techniques, the fittings were manufactured between the latter part of the 18th and the early 19th centuries, which might indicate that they were purchased in the course of 19th century weapons trade to be used on board the Egyptian ship.     

Convex envelope results and strong formulations for a class of mixed-integer programs

In this article we present a novel technique for deriving the convex envelope of certain nonconvex fixed-charge functions of the type that arise in several related applications that have been considered in the literature. One common attribute of these problems is that they involve choosing levels for the undertaking of several activities. Two or more activities share a common resource, and a fixed charge is incurred when any of these activities is undertaken at a positive level. We consider nonconvex programming formulations for these problems in which the fixed charges are expressed in the form of concave functions. With the use of the developed convex envelope results, we show that the convex envelope relaxations of the nonconvex formulations lead to the linear programming relaxations of the strong IP/MIP formulations of these problems. Moreover, our technique for deriving convex envelopes offers a useful construct that could be exploited in other related contexts as well. © 1996 John Wiley & Sons, Inc.     

A class of Bayes-optimal two-stage screens

Items are characterized by a set of attributes (T) and a collection of covariates (X) associated with those attributes. We wish to screen for acceptable items (T ∈ C_T), but T is expensive to measure. We envisage a two-stage screen in which observation of X_ is used as a filter at the first stage to sentence most items. The second stage involves the observation of T for those items for which the first stage is indecisive. We adopt a Bayes decision-theoretic approach to the development of optimal two-stage screens within a general framework for costs and stochastic structure. We also consider the important question of how much screens need to be modified in the light of resource limitations that bound the proportion of items that can be passed to the second stage. © 1996 John Wiley & Sons, Inc.