Maximizing the sum of certain quasiconcave functions using generalized benders decomposition

In this paper we consider the problem of maximizing the sum of certain quasi-concave functions over a convex set. The functions considered belong to the classes of functions which are known as nonlinear fractional and binonlinear functions. Each individual function is quasi-concave but the sum is not. We show that this nonconvex programming problem can be solved using Generalized Benders Decomposition as developed by Geoffrion.     

Variations on a cutting plane method for solving concave minimization problems with linear constraints

A cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts. This paper relates the question of finiteness of Tui's method to the so-called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method. The paper then presents several branch-and-bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed-charge transportation problem.     

Inference from accelerated life tests using eyring type re-parameterizations

Least squares estimators of the parameters of the generalized Eyring Model are obtained by using data from censored life tests conducted at several accelerated environments. These estimators are obtained after establishing that the Gauss-Markov conditions for least squares estimation are satisfied. Confidence intervals for the hazard rate at use conditions are obtained after empirically showing that the logarithm of the estimate of the hazard rate at use conditions is approximately normally distributed. The coverage probabilities of the confidence intervals are also verified by a Monte Carlo experiment. The techniques are illustrated by an application to some real data.     

Nuclear weapons,existential threats,and the stability–instability paradox

Recent scholarship has largely ignored systematic differences in the existential threats that nuclear-weapon possessors pose to other states. This study theorizes that the capacity to pose existential threats shapes nuclear-armed states’ willingness to use military force against one another. We explore three hypotheses regarding how nuclear-based existential threats can deter conflict or encourage it, including under the conditions proposed by the stability–instability paradox. We rely on a statistical analysis of nuclear-armed dyads from 1950 to 2001 and employ the Nuclear Annihilation Threat (NAT) Index to capture variation in the existential threats nuclear-armed states pose to one another. We find that being able to pose an existential threat to another state emboldens potential initiators to use military force but does not deter attacks. The emboldening effects are particularly strong under the hypothesized conditions of the stability–instability paradox. Our study provides unique contributions to ongoing debates over the political effects of nuclear weapons.     

A branch and bound algorithm for solving a class of nonlinear integer programming problems

This article presents a branch and bound method for solving the problem of minimizing a separable concave function over a convex polyhedral set where the variables are restricted to be integer valued. Computational results are reported.     

Properties of a multifacility location problem involving euclidian distances

This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.     

Some branch-and-bound procedures for fixed-cost transportation problems

In this article we present three properties that will improve the performance of branch-and-bound algorithms for fixed-cost transportation problems. By applying Lagrangian relaxation we show that one can develop stronger up and down penalties than those traditionally used and also develop a strengthened penalty for nonbasic variables. We also show that it is possible to “look ahead” of a particular node and determine the solution at the next node without actually calculating it. We present computational evidence by comparing our developments with existing procedures.     

Serious Rules for Nuclear Power Without Proliferation

The authors propose five principles for addressing the major deficiencies of the current treaty-based approach to nonproliferation. These involve: effectively closing the door to withdrawals from the Treaty on the Non-Proliferation of Nuclear Weapons (NPT); defining which nuclear technologies fall within the NPT's “inalienable right” provision, so as to maintain a reasonable safety margin against possible military application; expansion of International Atomic Energy Agency inspections to include greater readiness to use its “special” inspection authority; creation of an NPT enforcement regime, to include a secretariat; and universalizing the NPT so as to apply to all states, while creating a path for current non-parties to come into compliance. There is no illusion here about the prospects for the adoption of this approach. At a minimum, the world needs to be frank about the gap between nuclear programs and current nonproliferation protection. Encouragement of greater use of nuclear power should be predicated on closing that gap.