WorldCat Identities

Gay, David M.

Overview
Works: 37 works in 136 publications in 1 language and 632 library holdings
Genres: Handbooks and manuals 
Roles: Author
Classifications: QA402.5, 519.702855133
Publication Timeline
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Most widely held works by David M Gay
AMPL : a modeling language for mathematical programming by Robert Fourer( Book )

61 editions published between 1993 and 2009 in English and held by 426 WorldCat member libraries worldwide

AMPL, a modeling language for mathematical programming : using the AMPL student edition under MS-DOS by Robert Fourer( Book )

11 editions published in 1993 in English and held by 17 WorldCat member libraries worldwide

An adaptive nonlinear least-squares algorithm by J. E Dennis( Book )

11 editions published between 1977 and 1980 in English and Undetermined and held by 12 WorldCat member libraries worldwide

NL2SOL is a modular program for solving the nonlinear least-squares problem that incorporates a number of novel features. It maintains a secant approximation S to the second-order part of the least-squares Hessian and adaptively decides when to use this approximation. We have found it very helpful to "size" S before updating it, something which looks much akin to Oren-Luenberger scaling. Rather than resorting to line searches or Levenberg-Marquardt modifications, we use the double-dogleg scheme of Dennis and Mei together with a special module for assessing the quality of the step thus computed. We discuss these and other ideas behind NLZSOL and briefly describe its evolution and current implementation
AMPL : a modeling language for mathematical programming by Robert Fourer( Book )

4 editions published in 1993 in English and held by 7 WorldCat member libraries worldwide

Brown's method and some generalizations, with applications to minimization problems by David M Gay( Book )

4 editions published between 1975 and 1985 in English and held by 6 WorldCat member libraries worldwide

On solving robust and generalized linear regression problems by David M Gay( Book )

2 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide

Computing optimal locally constrained steps by David M Gay( Book )

2 editions published in 1979 in English and held by 4 WorldCat member libraries worldwide

Implementing Brown's method by David M Gay( Book )

3 editions published in 1975 in English and Undetermined and held by 4 WorldCat member libraries worldwide

AMPL : a mathematical programming language by Robert Fourer( Book )

2 editions published between 1987 and 1989 in English and held by 3 WorldCat member libraries worldwide

On convergence testing in model/trust-region algorithms for unconstrained optimization by David M Gay( Book )

2 editions published in 1982 in Undetermined and English and held by 3 WorldCat member libraries worldwide

AMPL PC student Version 2( )

1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide

Some convergence properties of Broyden's method by David M Gay( Book )

4 editions published in 1977 in English and Undetermined and held by 2 WorldCat member libraries worldwide

In 1965 Broyden introduced a family of algorithms called(rank-one) quasi-New-ton methods for iteratively solving systems of nonlinear equations. We show that when any member of this family is applied to an n x n nonsingular system of linear equations and direct-prediction steps are taken every second iteration, then the solution is found in at most 2n steps. Specializing to the particular family member known as Broyden - good) method, we use this result to show that Broyden's method enjoys local 2n-step Q-quadratic convergence on nonlinear problems
AMPL student edition( )

1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide

On Scolnik's proposed polynomial-time linear programming algorithm by David M Gay( Book )

2 editions published in 1973 in Undetermined and English and held by 2 WorldCat member libraries worldwide

Solving systems of nonlinear equations by Broyden's method with projected updates by David M Gay( Book )

3 editions published in 1977 in English and held by 1 WorldCat member library worldwide

We introduce a modification of Broyden's method for finding a zero of n nonlinear equations in n unknowns when analytic derivatives are not available. The method retains the local Q-superlinear convergence of Broyden's method and has the additional property that if any or all of the equations are linear, it locates a zero of these equations in n+1 or fewer iterations. Limited computational experience suggests that our modification often improves upon Eroyden's method
Representing Symmetric Rank Two Updates by David M Gay( )

1 edition published in 1976 in English and held by 0 WorldCat member libraries worldwide

"Various quasi-Newton methods periodically add a symmetric "correction" matrix of rank at most 2 to a matrix approximating some quantity A of interest (such as the Hessian of an objective function). In this paper we examine several ways to express a symmetric rank 2 matrix [delta] as the sum of rank 1 matrices. We show that it is easy to compute rank 1 matrices [delta1] and [delta2] such that [delta] = [delta1] + [delta2] and [the norm of delta1]+ [the norm of delta2] is minimized, where "." is any inner product norm. Such a representation recommends itself for use in those computer programs that maintain A explicitly, since it should reduce cancellation errors and/or improve efficiency over other representations. In the common case where [delta] is indefinite, a choice of the form [delta1] = [delta2 to the power of T] = [xy to the power of T] appears best. This case occurs for rank 2 quasi- Newton updates [delta] exactly when [delta] may be obtained by symmetrizing some rank 1 update; such popular updates as the DFP, BFGS, PSB, and Davidon's new optimally conditioned update fall into this category"--NBER website
Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 4.0 developers manual( )

1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes
DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 4.0 reference manual( )

1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications
On Modifying Singular Values to Solve Possible Singular Systems of Non-Linear Equations( )

2 editions published in 1976 in English and held by 0 WorldCat member libraries worldwide

We show that if a certain nondegeneracy assumption holds, it is possible to guarantee the existence of a solution to a system of nonlinear equations f(x) = 0 whose Jacobian matrix J(x) exists but maybe singular. The main idea is to modify small singular values of J(x) in such away that the modified Jacobian matrix J(x) has a continuous pseudoinverse J+(x)and that a solution x of f(x) = 0 may be found by determining an asymptote of the solution to the initial value problem x(0) = x[sub0}, x¿h Ø?0@1A0?(Øt) = -J+(x)f(x). We briefly discuss practical (algorithmic) implications of this result. Although the nondegeneracy assumption may fail for many systems of interest (indeed, if the assumption holds and J(x) is non-singular, then x is unique), algorithms using(x) may enjoy a larger region of convergence than those that require(an approximation to) J[to the -1 power[(x)
DAKOTA, a multilevel parellel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 4.0 uers's manual( )

1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the DAKOTA software and provides capability overviews and procedures for software execution, as well as a variety of example studies
 
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AMPL : a modeling language for mathematical programming
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English (114)

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