Two new unconstrained optimization algorithms which use function and gradient values

Dennis, John E.; Mei, Huayue

doi:10.1007/bf00932218

Cited by 173 publications

(104 citation statements)

References 3 publications

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“…The maximization is performed using a general quasi-Newton procedure (Dennis, Gay, and Welsch 1981;Dennis and Mei 1979) obtained from Netlib. Standard error estimates are calculated by inverting the observed information matrix.…”

Section: Brief Overview: Derivation Of the Likelihoodmentioning

confidence: 99%

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

Jones

Nagin

Roeder

2001

Sociological Methods & Research

2,057

2,108

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This article introduces a new SAS procedure written by the authors that analyzes longitudinal data (developmental trajectories) Patterson et al. 1998;Patterson and Yoerger 1997;Sampson and Laub 1993). This article demonstrates a new SAS procedure, called TRAJ, developed by the authors for estimating developmental trajectories. The procedure is based on a semiparametric, group-based modeling strategy. Technically, the model is a mixture of probability distributions that are suitably specified to describe the data to be analyzed. The approach is intended to complement two well-established methods for analyzing developmental trajectories-hierarchical modeling (Bryk and Raudenbush 1987, 1992;Goldstein 1995) and latent growth curve modeling (Meredith and Tisak 1990;Muthen 1989;Willett and Sayer 1994). In hierarchical modeling, individual variation in developmental trajectories, which are commonly called growth curves, are captured by a random coefficients modeling strategy.

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Section: Brief Overview: Derivation Of the Likelihoodmentioning

confidence: 99%

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

Jones

Nagin

Roeder

2001

Sociological Methods & Research

2,057

2,108

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“…Necessary and sufficient conditions for this solution are The most popular is the dog-leg method [25], [4], where If B is not sufficiently sparse, then the sparse Choleski decomposition of B is expensive. In this case, iterative methods based on conjugate gradients are more suitable.…”

Section: Methods For Solving Large-scale Trust-region Subproblemsmentioning

confidence: 99%

Efficient methods for large-scale unconstrained optimization

Lukšan

Vlček

2006

Nonconvex Optimization and Its Applications

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Abstract:This contribution contains a description of efficient methods for large-scale unconstrained optimization. Many of them have been developed recently by the authors. It concerns limited memory methods for general smooth optimization, variable-metric bundle methods for partially separable nonsmooth optimization, hybrid methods for sparse least squares and methods for solving large-scale trust-region subproblems. These methods are compared with other methods by extensive computational experiments.

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“…The minimizer used by the procedure is MINOP (Dennis & Mei, 1975), a modification of Powell's (1970a,b) dog-leg strategy which appears to be powerful and quite efficient. where (xt, Yt, Zt) are the coordinates of every atom before rotation, (x~,y~,zc) are the corresponding coordinates after rotation (the final coordinates) and a, fl, y are the Euler rotational angles, chosen according to the convention generally used in the quantum theory of angular momentum (Arfken, 1970).…”

Section: Methodsmentioning

confidence: 99%

“…At the present time, the Diamond or WGS procedures have been used most widely for applications of model building to proteins. This paper will describe a new model-building procedure, which remedies certain problems common to both the Diamond (1966) and WGS methods, employs a powerful minimizer (Dennis & Mei, 1975), and retains most of the ease of use of the WGS procedure. In practice, the new method requires a certain amount of operator intervention in decision-making processes, but the intervention is largely routine and, in some cases, enables the improvement of the fitting to be greatly accelerated.…”

Section: Introductionmentioning

confidence: 99%

A model-building procedure with particular application to proteins

Fitzwater¹,

Scheraga²

1980

Acta Cryst Sect A

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A procedure for fitting a molecular model with fixed bond lengths and bond angles to a set of Cartesian coordinates has been developed. This procedure is designed to fit coordinates obtained from an X-ray electron-density map, although it can also fit coordinate sets from other sources. It differs from other model-building methods which use fixed bond lengths and bond angles in that it takes cognizance of certain information present in the electron-density map, which is ignored in other methods. The inherent uncertainty in the values of the coordinates determined from the map influences the fitting; i.e., if the computed location of an atom of the model is within the uncertainty assigned to the corresponding coordinate derived from the map, the fit of the atom of the model is assigned as exact. Also, the fitting process may begin anywhere along the molecular chain, in contrast to other procedures which commence fitting at or near one end of the chain. Thus, the present procedure can avoid errors that might arise if the starting point were chosen in a region where the atoms are poorly defined, as they often are at the ends of the chain. The procedure is designed to be used with a large amount of operator intervention, making it fairly flexible. Complete mathematical details of the method are given. A Fortran IV computer program using the method to fit a polypeptide model to a set of Cartesian coordinates has been written. The program has been used to fit a model of bovine pancreatic trypsin inhibitor to Cartesian coordinates derived from the 2-5 A resolution electron-density map. The r.m.s. deviation between the model and the weighted coordinates from the map was 0.49 A. As a preliminary step in a refinement of the 2.5 A structure by potentialenergy-constrained model building, the model obtained here was subjected to energy minimization with the atomic coordinates constrained to remain 'close' to the original guide points.

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Two new unconstrained optimization algorithms which use function and gradient values

Cited by 173 publications

References 3 publications

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

Efficient methods for large-scale unconstrained optimization

A model-building procedure with particular application to proteins

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