Recent progress in unconstrained nonlinear optimization without derivatives

We present an introduction to a new class of derivative free methods for unconstrained optimization. We start by discussing the motivation for such methods and why they are in high demand by practitioners. We then review the past developments in this field, before introducing the features that characterize the newer algorithms. In the context of a trust region framework, we focus on techniques that ensure a suitable “geometric quality” of the considered models. We then outline the class of algorithms based on these techniques, as well as their respective merits. We finally conclude the paper with a discussion of open questions and perspectives. Current reports available by anonymous ftp from the directory “pub/reports” on thales.math.fundp.ac.be. WWW: http://www.fundp.ac.be/ phtoint/pht/publications.html.     

The High‐Throughput Synthesis and Phase Characterisation of Amphiphiles: A Sweet Case Study

A new method for the discovery of amphiphiles by using high‐throughput (HT) methods to synthesise and characterise a library of galactose‐ and glucose‐containing amphiphilic compounds is presented. The copper‐catalysed azide–alkyne cycloaddition (CuAAC) “click” reaction between azide‐tethered simple sugars and alkyne‐substituted hydrophobic tails was employed to synthesise a library of compounds with systematic variations in chain length and unsaturation in a 24‐vial array format. The liquid–crystalline phase behaviour was characterised in a HT manner by using synchrotron small‐angle X‐ray scattering (SSAXS). The observed structural variation with respect to chain parameters, including chain length and degree of unsaturation, is discussed, as well as hydration effects and degree of hydrogen bonding between head groups. The validity of our HT screening approach was verified by resynthesising a short‐chain glucose amphiphile. A separate phase analysis of this compound confirmed the presence of numerous lyotropic liquid–crystalline phases.     

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.     

Computational Investigation of the Substituent Effect on the Intramolecular Proton Transfer Reaction of 3-Hydroxytropolone

The effects of substituent type and position on the proton transfer reaction of 3-hydroxytropolone(3-OHTRN) have been investigated theoretically by using density functional theory at the level of B3LYP/ 6-31+G** method. The influence of solvent on the proton transfer reactions of substituted 3-OHTRN has been examined using the self-consistent isodensity polarized continuum model(SCI-PCM) in water. As a result, while the proton transfer reaction is kinetically the easiest by substitution on position 3 of-NH2 group in the gas phase, it is kinetically the easiest by substitution on position 5 of the same group in water. In addition, these reactions are either kinetically or thermodynamically easier in the gas phase than that in water, except the reaction of structure with-NH2 group at position 6.     

MAOS protocols for the general synthesis and lead optimization of 3,6-disubstituted-[1,2,4]triazolo[4,3-b]pyridazines

General, high-yielding MAOS protocols for the expedient synthesis of functionalized 3,6-disubstituted-[1,2,4]triazolo[4,3-b]pyridazines are described amenable to an iterative analog library synthesis strategy for the lead optimization of an M1 antagonist screening hit. Optimized compounds proved to be highly selective M1 antagonists.     

Role of the dopant in the superconductivity of diamond

We present an ab initio study of the recently discovered superconductivity of boron doped diamond within the framework of a phonon-mediated pairing mechanism. The role of the dopant, in substitutional position, is unconventional in that half of the coupling parameter lambda originates in strongly localized defect-related vibrational modes, yielding a very peaked Eliashberg alpha2F(omega) function. The electron-phonon coupling potential is found to be extremely large, and T(C) is limited by the low value of the density of states at the Fermi level. The effect of boron isotope substitution is explored.     

Experimental evidence of intermittent convection in the edge of magnetic confinement devices

Probe measurements in the PISCES linear device indicate the presence of plasma radially far from where it is produced. We show that this is mainly caused by large-scale structures of plasma with high radial velocity. Data from the Tore Supra tokamak show striking similarities in the shape of these intermittent events as well as the fluctuation density probability distribution and frequency spectrum. The fact that intermittent, large-scale events are so similar in linear devices and tokamaks indicates the universality of convective transport in magnetically confined plasmas.     

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.     

Superconductivity in doped sp3 semiconductors: the case of the clathrates

We present a joint experimental and theoretical study of the superconductivity in doped silicon clathrates. The critical temperature in Ba(8)@Si-46 is shown to strongly decrease with applied pressure. These results are corroborated by ab initio calculations using MacMillan's formulation of the BCS theory with the electron-phonon coupling constant lambda calculated from perturbative density functional theory. Further, the study of I(8)@Si-46 and of gedanken pure silicon diamond and clathrate phases doped within a rigid-band approach show that the superconductivity is an intrinsic property of the sp(3) silicon network. As a consequence, carbon clathrates are predicted to yield large critical temperatures with an effective electron-phonon interaction much larger than in C60.     

A projected newton method forl p norm location problems

This paper is concerned with the numerical solution of continuous minisum multifacility location problems involving thel _p norm, where 1<p<x. This class of problems is potentially difficult to solve because the objective function is not everywhere diflerentiable. After developing conditions that characterize the minimum of the problems under consideration, a second-order algorithm is presented. This algorithm is based on the solution of a finite sequence of linearly constrained subproblems. Descent directions for these subproblems are obtained by projecting the Newton direction onto the corresponding constraint manifold. Univariate minimization is achieved via a specialized linesearch which recognizes the possibility of first derivative discontinuity (and second derivative unboundedness) at points along the search direction. The algorithm, motivated by earlier works of Calamai and Conn, and related to methods recently described by Overton and Dax, is shown to possess both global and quadratic convergence properties. Degeneracy can complicate the numerical solution of the subproblems. This degeneracy is identified, and a method for handling it is outlined. An implementation of the algorithm, that exploits the intrinsic structure of the location problem formulation, is then described along with a discussion of numerical results. The research was supported in part by Natural Sciences and Engineering Research Council of Canada grants A-5671 and A-8639 and by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38. This paper was typeset using software developed at Bell Laboratories and the University of California at Berkeley.