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.     

Effects of viscosity on droplet formation and mixing in microfluidic channels

This paper characterizes the conditions required to form nanoliter-sized droplets (plugs) of viscous aqueous reagents in flows of immiscible carrier fluid within microfluidic channels. For both non-viscous (viscosity of 2.0 mPa s) and viscous (viscosity of 18 mPa s) aqueous solutions, plugs formed reliably in a flow of water-immiscible carrier fluid for Capillary number less than 0.01, although plugs were able to form at higher Capillary numbers at lower ratios of the aqueous phase flow rate to the flow rate of the carrier fluid (in all the experiments performed, the Reynolds number was less than 1). The paper also shows that combining viscous and non-viscous reagents can enhance mixing in droplets moving through straight microchannels by providing a nearly ideal initial distribution of reagents within each droplet. The study should facilitate the use of this droplet-based microfluidic platform for investigation of protein crystallization, kinetics, and assays.     

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...     

Isothiocyanatochloromethylphosphonates and Phosphinates – Versatile Synthones for Obtaining of S (Se), N,P–Containing Heterocycles

Abstract

Isothiocyanatochloromethyl(thio)phosphonates and (thio)-phosphinates 1 (X=O, S; R¹ = OPh, CH₂Cl, NCS; R² = H, Cl have been found to be convenient starting material for synthesis of a variety of S (Se), N, P-containing cyclic compounds. They react with different proton containing nucleophiles in the presence of a base with formation of saturated 2 and unsaturated 3 five membered phosphacyclanes. Diisothiocyanatodichloromethylphosphonates 1 (R¹ = NCS, R² =Cl) produce with amines and thiols appropriate bicyclic compounds 4.     

Structural Transformations of Ni1 – xCuxFe2O4 Nanoparticles Depending on the Number of Cu Ions

Physics of the Solid State - Changes in the structure and properties of the Ni1 – xCuxFe2O4 ferrites-spinel magnetic nanoparticles depending on the Cu ion concentration (0...     

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.