A new approach to variable metric algorithms

Fletcher, R.

doi:10.1093/comjnl/13.3.317

Cited by 3,452 publications

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“…In all techniques, Bmax and other model parameters were fitted using a system for function optimization (James and Roos, 1976). The simplex algo rithm (NeIder and Mead, 1965) and subsequently the vari able metric method of Fletcher (1970) were used as opti mization techniques. The simplex method of NeIder and Mead is rather insensitive to local minima, statistical, and rounding errors.…”

Section: Discussionmentioning

confidence: 99%

The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography

Jovkar¹,

Wienhard²,

Pawlik³

et al. 1990

J Cereb Blood Flow Metab

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Summary:We used the ligand 3-N-[2,-18F]fluoroethyl spiperone (FESP), which binds to Dz-dopamine receptors in the striatum, and positron emission tomography (PET) to quantify striatal Dz-dopamine densities (Bmax) and binding kinetics in baboon brain in vivo. Sequential PET scans were obtained for 4 h post injection. Various similar models based on a nonlinear kinetic four-compartment model that takes into account the effect of ligand specific activity were used. We investigated the effect of exact model configuration on the reliability of Bmax and other kinetic transfer coefficients. We found that with the ligand FESP and dynamic PET studies, the estimated val ues of Bmax and other model parameters are sensitive to the choice of model configuration, ligand specific activPositron emission tomography (PET) with appro priate positron-emitting ligands allows the in vivo imaging and quantitation of neuroreceptors (Huang et aI. , 1986; Sedval et aI. , 1986;Gjedde and Wong, 1987;Swart and Korf, 1987). As a receptor class, D2-dopaminergic receptors have received much in terest since they have been implicated in a number of neurologic and psychiatric disorders. Recent PET investigations have reported modifications of Drreceptor densities in schizophrenia (Wong et aI., 1986), progressive supranuclear palsy (Baron et aI. , 1986), and normal aging (Wong et aI. , 1984; Baron et aI. , 1986).Received July 19, 1989; revised February 15, 1990; accepted March 13, 1990.Address correspondence and reprint requests to Dr. K. Wien hard at Max-Planck-Institut fii r Neurologische Forschung, PET Labor, Haus 30, Joseph-Stelzmann-Str. 9, 5000 Koln 41 (Lin denthal), F.R.G. In this study, we used the ligand 3-N-[2,_18F] fluoroethylspiperone (FESP) to quantitate neurore ceptor densities (Bmax) and affinities in baboon stri atum by PET. The ligand FESP binds to D2-dopamine receptors in the striatum (Satyamurthy et aI. , 1986; Coenen et aI. , 1987). We investigated the effect of model configuration and ligand specific ac tivity on the reliability of D2-dopamine receptor density and affinity estimates. This was done by analysis of a series of studies in the same baboon with different ligand specific activities and with var ious model configurations based on a comprehen sive four compartment model similar to that pro posed by Huang et al. (1986). Using this kinetic model, we also obtained an estimate of transfer co efficients.Simulation studies were carried out to study the effect of using ligands with different binding char acteristics and with various specific activities on estimated receptor densities in human studies. The use of multiple-injection studies is not warranted in

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Section: Discussionmentioning

confidence: 99%

The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography

Jovkar¹,

Wienhard²,

Pawlik³

et al. 1990

J Cereb Blood Flow Metab

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“…Os modelos foram obtidos a partir dos dados cristalográficos 31 . Os parâmetros geométricos das moléculas de CO, CO 2 e NH 3 foram totalmente otimizados, utilizando o algoritmo Broyden-Fletcher-Goldfarb-Shanno (BFGS) [63][64][65][66] , enquanto que os parâmetros geométricos do "cluster" foram mantidos congelados. Os efeitos da otimização não deixam de ser importantes, entretanto, os modelos estudados têm grande número de áto-mos e, conseqüentemente, elevado grau de liberdade.…”

Section: Modelos E Métodosunclassified

Análise teórica da interação de CO, CO2 e NH3 com ZnO

Martins¹,

Vasconcellos

Longo³

et al. 2004

Quím. Nova

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Recebido em 1/10/02; aceito em 16/7/03 THEORETICAL ANALYSIS OF THE INTERACTION OF CO, CO 2 , AND NH 3 WITH ZnO. This paper presents a study of the interaction of small molecules with ZnO surfaces by means of theoretical methods. The AM1 semi-empirical method was used for optimizing the geometric parameters of adsorbed molecules. The optimized AM1 structures were used in the calculations of the ab initio RHF method with the 3-21G* basis set. The interaction of CO, CO 2 and NH 3 molecules were studied with (ZnO) 22 and (ZnO) 60 cluster models. We have analyzed the interaction energy, SCF orbital energies, Mulliken charges and the density of states (DOS).Keywords: zinc oxide; interaction; theoretical methods. INTRODUÇÃOO óxido de zinco tem sido alvo de inúmeras pesquisas no decorrer dos últimos anos 1,2 com uma importante aplicação em materiais eletrônicos, tais como, células foto-voltaicas 1 , varistores 2,3 , além da grande diversidade de aplicações relacionadas a defeitos 4,5 , catálise 6-12 , sensores de gases 13 e quimissorção 14 . Superfícies de óxidos são sistemas de especial importância em ciências dos materiais 15,16 , dentre as quais, a superfície do ZnO tem uma diversificada atividade catalítica para um grande número de reações. A maioria dos catalisadores comerciais consiste de pequenas partículas de metal em grandes superfícies de óxidos, onde o metal é a fase ativa e os óxidos podem se comportar como materiais inertes ou modificar a atividade do metal, interagindo através de ligações 17,18 . Em outros, os óxidos formam parte da fase ativa onde a atividade catalítica total do sistema é determinada por interações cooperativas, que envolvem o metal e sítios ativos do óxido. Um completo entendimento destes sistemas catalíticos requer uma compreensão detalhada dos fatores que determinam as interações entre os vários constituintes: metal ↔ óxido, metal ↔ adsorvato e óxido ↔ adsorvato 19 O ZnO também é considerado um consagrado varistor, isto é, um dispositivo eletrônico de proteção contra sobrecarga de tensão ou ainda um dispositivo de descarga elétrica, que possui um elevado índice de não linearidade 30 . Suas propriedades elétricas dependem da microestrutura final do material que, por sua vez, pode ser controlada por diversos parâmetros físico-químicos, tais como processamento utilizado, temperatura de sinterização, taxa de aquecimento e resfriamento e natureza química dos dopantes. O ZnO é também um excelente protótipo para o estudo de estrutura eletrônica de interfaces e propriedades de transportes em óxidos semicondutores 1,3 .O ZnO cristaliza-se em uma estrutura hexagonal do tipo wurtizita, na qual cada átomo de zinco está no centro de um tetraedro distorcido coordenado a quatro outros oxigênios vizinhos 31 . Existem três superfícies naturais: a polar terminada em Zn, o plano hexagonal (0001), onde os íons zinco estão posicionados para fora, o plano polar (0001 -) terminado em oxigênio, onde os íons oxigênio estão posicionados para fora e o plano não polar prismático (101 -0) onde ambos, zinco e oxig...

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“…Quasi-Newton methods for unconstrained optimization are important computational tools in many scientific fields and are a standard subject in textbooks on computation. The BFGS method, proposed individually in [6], [14], [20], and [30], is implemented in most optimization software and is widely recognized as efficient. Generalizations of BFGS are available for large problems with memory limitations, for problems with bound constraints, and for a parallel computing environment.…”

Section: Ams Subject Classifications 65k10 90c53mentioning

confidence: 99%

“…This is known as DFP [13], [18] and is generally regarded as inferior to BFGS. Fletcher [14] advocated restricting attention to Broyden updates that are convex combinations of the BFGS and DFP updates because such updates satisfy a monotone eigenvalue property when used to minimize quadratic functions. Recently, however, various choices of negative Broyden parameters (φ k < 0 corresponding to λ k < 1) have been studied.…”

Section: Historical Developments Crockett and Chernoffmentioning

confidence: 99%

Statistical Quasi-Newton: A New Look at Least Change

Liu¹,

Wiel²

2008

SIAM J. Optim.

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Abstract.A new method for quasi-Newton minimization outperforms BFGS by combining least-change updates of the Hessian with step sizes estimated from a Wishart model of uncertainty. The Hessian update is in the Broyden family but uses a negative parameter, outside the convex range, that is usually regarded as the safe zone for Broyden updates. Although full Newton steps based on this update tend to be too long, excellent performance is obtained with shorter steps estimated from the Wishart model. In numerical comparisons to BFGS the new statistical quasi-Newton (SQN) algorithm typically converges with about 25% fewer iterations, functions, and gradient evaluations on the top 1/3 hardest unconstrained problems in the CUTE library. Typical improvement on the 1/3 easiest problems is about 5%. The framework used to derive SQN provides a simple way to understand differences among various Broyden updates such as BFGS and DFP and shows that these methods do not preserve accuracy of the Hessian, in a certain sense, while the new method does. In fact, BFGS, DFP, and all other updates with nonnegative Broyden parameters tend to inflate Hessian estimates, and this accounts for their observed propensity to correct eigenvalues that are too small more readily than eigenvalues that are too large. Numerical results on three new test functions validate these conclusions. Key words. BFGS, DFP, negative Broyden family, Wishart model AMS subject classifications. 65K10, 90C53DOI. 10.1137/040614700 1. Introduction. Quasi-Newton methods for unconstrained optimization are important computational tools in many scientific fields and are a standard subject in textbooks on computation. The BFGS method, proposed individually in [6], [14], [20], and [30], is implemented in most optimization software and is widely recognized as efficient. Generalizations of BFGS are available for large problems with memory limitations, for problems with bound constraints, and for a parallel computing environment. In theoretical investigations BFGS is known as a special case of the Broyden class [5]. Some Broyden updates with negative Broyden parameters have been found to produce faster convergence than BFGS updates [31], [8] but, for various reasons, have not been widely adopted. Indeed, Byrd et. al. conclude that "practical algorithms that preserve the excellent properties of the BFGS method are difficult to design." Nocedal and Wright [29] state that "the BFGS formula. . . is presently considered to be the most effective of all quasi-Newton updating formulae." In our opinion, BFGS remains the most popular front-runner because of two important unanswered

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A new approach to variable metric algorithms

Cited by 3,452 publications

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The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography

The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography

Análise teórica da interação de CO, CO2 e NH3 com ZnO

Statistical Quasi-Newton: A New Look at Least Change

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A new approach to variable metric algorithms

Cited by 3,452 publications

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The Quantitative Analysis of D2-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-18F]Fluoroethylspiperone Using Positron Emission Tomography

The Quantitative Analysis of D2-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-18F]Fluoroethylspiperone Using Positron Emission Tomography

Análise teórica da interação de CO, CO2 e NH3 com ZnO

Statistical Quasi-Newton: A New Look at Least Change

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The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography

The Quantitative Analysis of D₂-Dopamine Receptors in Baboon Striatum in vivo with 3-N-[2'-¹⁸F]Fluoroethylspiperone Using Positron Emission Tomography