Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.     

Magnetic and Mössbauer studies of L10–FePt/Fe/Ta multilayer structures

Physics of the Solid State - Magnetic L10–FePt(10 nm)/Fe(t, nm)/Ta(2 nm) (t is the Fe film thickness that is varied from 0 to 15 nm) multilayer structures have been prepared by magnetron...     

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.     

NMR magnetization transfer as a tool for characterization of nanoporous materials

The application of nuclear magnetic resonance magnetization transfer experiments to probe the surface-to-volume ratio and pore morphology of porous materials with characteristic pore sizes of 1-100 nm is described. The method is based on the phenomenon of incomplete freezing of liquids in small pores where a few monolayers adjacent to the pore walls remain liquid. Sufficient difference between the transverse relaxation times in the solid frozen core and liquid surface layer allows the initial preparation and subsequent re-equilibration of a solid-liquid magnetization grating. The method is demonstrated using model nanoporous materials with known characteristics. The ensuing problems of the mechanism of the magnetization transfer through the interface and within the frozen core are discussed and elucidated by pulsed-field-gradient NMR experiments.     

A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.     

Plug‐Based Microfluidics with Defined Surface Chemistry to Miniaturize and Control Aggregation of Amyloidogenic Peptides

Small with control : For miniaturization of protein aggregation experiments the interfacial chemistry must be controlled to avoid protein aggregation caused by interfacial adsorption. Plug‐based microfluidics with defined surface chemistry (see schematic picture) can then be used to perform hundreds of aggregation experiments with volume‐limited samples, such as cerebrospinal fluid from mice.

     

A physical organic mechanistic approach to understanding the complex reaction network of hemostasis (blood clotting)

This review focuses on how the mechanistic approach of physical organic chemistry can be used to elucidate the mechanisms behind complex biochemical networks. The dynamics of biochemical reaction networks is difficult to describe by considering their individual reactions, just as the dynamics of organic reactions is difficult to describe by considering individual electrons and atomic nuclei. Physical organic chemists have developed a useful set of tools to predict the outcome of organic reactions by separating the interacting molecules into modules (functional groups), and defining general rules for how these modules interact (mechanisms). This review shows how these tools of physical organic chemistry may be used to describe reaction networks. In addition, it describes the application of these tools to develop a mechanistic understanding of the dynamics of the complex network of hemostasis, which regulates blood clotting. Copyright © 2007 John Wiley & Sons, Ltd.     

Crystal structure, Fermi surface calculations and Shubnikov-de Haas oscillation spectrum of the organic metal θ-(BETS)4HgBr4(C6H5Cl) at low temperature

The organic metal θ-(BETS)₄HgBr₄(C₆H₅Cl) is known to undergo a phase transition as the temperature is lowered down to about 240 K. X-ray data obtained at 200 K indicate a corresponding modification of the crystal structure, the symmetry of which is lowered from quadratic to monoclinic. In addition, two different types of cation layers are observed in the unit cell. The Fermi surface (FS), which can be regarded as a network of compensated electron and hole orbits according to band structure calculations at room temperature, turns to a set of two alternating linear chains of orbits at low temperature. The field and temperature dependence of the Shubnikov-de Haas oscillation spectrum have been studied up to 54 T. Eight frequencies are observed which, in any case, point to an FS much more complex than predicted by band structure calculations at room temperature, even though some of the observed Fourier components might be ascribed to magnetic breakdown or frequency mixing. The obtained spectrum could result from either an interaction between the FSs linked to each of the two cation layers or to an eventual additional phase transition in the temperature range below 200 K.