A projection method forl p norm location-allocation problems

We present a solution method for location-allocation problems involving thel _p norm, where 1 <p < . The method relaxes the {0, 1} constraints on the allocations, and solves for both the locations and allocations simultaneously. Necessary and sufficient conditions for local minima of the relaxed problem are stated and used to develop an iterative algorithm. This algorithm finds a stationary point on a series of subspaces defined by the current set of activities. The descent direction is a projection onto the current subspace of a direction incorporating second-order information for the locations, and first-order information for the allocations. Under mild conditions, the algorithm finds local minima with {0, 1} allocations and exhibits quadratic convergence. An implementation that exploits the special structure of these problems to dramatically reduce the computational cost of the required numerical linear algebra is described. Numerical results for thirty-six test problems are included.This research was supported in part by Natural Sciences and Engineering Research Council (NSERC) of Canada grants A-5671 and A-8639, and by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No F49620-91-C-0079. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.Corresponding author.     

Suppression of temperature fluctuations and energy barrier generation by velocity shear

First measurements of temperature fluctuations in a region of high velocity shear show that absolute and normalized fluctuation levels are reduced across the shear layer, a result that is consistent with weak parallel electron thermal conduction in the electron temperature dynamics. The concomitant reduction of temperature, density, and electric field fluctuations reduces the anomalous conducted and convected heat fluxes.     

An exact penalty function for semi-infinite programming

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the ℓ₁ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result of the approximate quadrature rather than an a priori aspect of the model. This research was partially supported by Natural Sciences and Engineering Research Council of Canada grants A-8639 and A-8442. This paper was typeset using software developed at Bell Laboratories and the University of California at Berkeley.     

A pressure-jump time-resolved X-ray diffraction study of cubic-cubic transition kinetics in monoolein

In the past two decades, the geometric pathways involved in the transformations between inverse bicontinuous cubic phases in amphiphilic systems have been extensively theoretically modeled. However, little experimental data exists on the cubic-cubic transformation in pure lipid systems. We have used pressure-jump time-resolved X-ray diffraction to investigate the transition between the gyroid QGII and double-diamond QDII phases in mixtures of 1-monoolein in 30 wt % water. We find for this system that the cubic-cubic transition occurs without any detectable intermediate structures. In addition, we have determined the kinetics of the transition, in both the forward and reverse directions, as a function of pressure-jump amplitude, temperature, and water content. A recently developed model allows (at least in principle) the calculation of the activation energy for lipid phase transitions from such data. The analysis is applicable only if kinetic reproducibility is achieved, at least within one sample, and achievement of such kinetic reproducibility is shown here, by carrying out prolonged pressure-cycling. The rate of transformation shows clear and consistent trends with pressure-jump amplitude, temperature, and water content, all of which are shown to be in agreement with the effect of the shift in the position of the cubic-cubic phase boundary following a change in the thermodynamic parameters.     

A progressive barrier derivative-free trust-region algorithm for constrained optimization

We study derivative-free constrained optimization problems and propose a trust-region method that builds linear or quadratic models around the best feasible and around the best infeasible solutions found so far. These models are optimized within a trust region, and the progressive barrier methodology handles the constraints by progressively pushing the infeasible solutions toward the feasible domain. Computational experiments on 40 smooth constrained problems indicate that the proposed method is competitive with COBYLA, and experiments on two nonsmooth multidisciplinary optimization problems from mechanical engineering show that it can be competitive with the NOMAD software.     

A network penalty method

We consider the minimum cost network flow problem and describe how the non-linear penalty function methods of Conn and Bartels can be specialized to a combinatorial algorithm for this problem. We report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable. The algorithm can be proven finite using a modification of Cunningham's strongly feasible basis pivoting rule.Supported by the Natural Sciences and Engineering Research Council of Canada, and the joint research project Combinatorial Optimization of the Natural Sciences and Engineering Research Council, Canada and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).