检索结果-内蒙古大学图书馆

SQUARE-ROOT variable-metric methods FOR MINIMIZATION

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第3期21卷 251-259页

作者： HULL, DG TAPLEY, BD UNIV TEXAS DEPT AEROSP ENGN & ENGN MECHAUSTINTX 78712

variable-metric methods are presented which do not need an accurate one-dimensional search and eliminate roundoff error problems which can occur in updating the metric for large-dimension systems. The methods are based on updating the square root of the metric, so that a positive-definite metric always results. The disadvantage of intentionally relaxing the accuracy of the one-dimensional search is that the number of iterations (and hence, gradient evaluations) increases. For problems involving a large number of variables, the square-root method is presented in a triangular form to reduce the amount of computation. Also, for usual optimization problems, the square-root procedure can be carried out entirely in terms of the metric, eliminating storage and computer time associated with computations of the square root of the metric.

关键词： function minimization mathematical programming Nonlinear programming parameter optimization variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

DIRECT PREDICTION methods IN HILBERT-SPACE WITH APPLICATIONS TO CONTROL PROBLEMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第3期22卷 399-415页

作者： HUNTLEY, E TURNER, PR UNIV SHEFFIELD DEPT APPL MATH & COMP SCISHEFFIELDENGLAND UNIV LANCASTER DEPT MATHLANCASTER LA1 4YBLANCASHIREENGLAND

In this paper, the convergence of variable-metric methods without line searches (direct prediction methods) applied to quadratic functionals on a Hilbert space is established. The methods are then applied to certain control problems with both free endpoints and fixed endpoints. Computational results are reported and compared with earlier results. The methods discussed here are found to compare favorably with earlier methods involving line searches and with other direct prediction quasi-Newton methods.

关键词： control theory Hilbert spaces optimization theorems variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

DIRECT-PREDICTION QUASI-NEWTON methods IN HILBERT-SPACE WITH APPLICATIONS TO CONTROL PROBLEMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第2期21卷 199-211页

作者： TURNER, PR HUNTLEY, E UNIV LANCASTER DEPT MATHLANCASTER LA1 4YQLANCASHIREENGLAND UNIV SHEFFIELD DEPT APPL MATH & COMP SCISHEFFIELD S10 2TNYORKSHIREENGLAND

In this paper, the Hilbert-space analogue of a result of Huang, that all the methods in the Huang class generate the same sequence of points when applied to a quadratic functional with exact linear searches, is established. The convergence of a class of direct prediction methods based on some work of Dixon is then proved, and these methods are then applied to some control problems. Their performance is found to be comparable with methods involving exact linear searches.

关键词： control theory Hilbert spaces optimization theorems variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

Numerical infinitesimals in a variable metric method for convex nonsmooth optimization

引用

APPLIED MATHEMATICS AND COMPUTATION 2018年 318卷 312-320页

作者： Gaudioso, Manlio Giallombardo, Giovanni Mukhametzhanov, Marat Univ Calabria Arcavacata Di Rende Italy Lobachevsky State Univ Nizhnii Novgorod Russia

The objective of the paper is to evaluate the impact of the infinity computing paradigm on practical solution of nonsmooth unconstrained optimization problems, where the objective function is assumed to be convex and not necessarily differentiable. For such family of problems, the occurrence of discontinuities in the derivatives may result in failures of the algorithms suited for smooth problems. We focus on a family of nonsmooth optimization methods based on a variable metric approach, and we use the infinity computing techniques for numerically dealing with some quantities which can assume values arbitrarily small or large, as a consequence of nonsmoothness. In particular we consider the case, treated in the literature, where the metric is defined via a diagonal matrix with positive entries. We provide the computational results of our implementation on a set of benchmark test-problems from scientific literature. (C) 2017 Elsevier Inc. Allrights reserved.

关键词： Nonsmooth optimization Infinity computing variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

STATE-OF-THE-ART IN PARALLEL NONLINEAR OPTIMIZATION

引用

PARALLEL COMPUTING 1988年第2期6卷 133-155页

作者： LOOTSMA, FA RAGSDELL, KM UNIV MISSOURI CTR DESIGN PROD 1080 ENGN COLUMBIA MO 65211 USA

This survey is concerned with variants of nonlinear optimization methods designed for implementation on parallel computers. First, we consider a variety of methods for unconstrained minimization. We consider a particular type of parallelism (simultaneous function and gradient evaluations), and we concentrate on the main sources of inspiration: conjugate directions, homogeneous functions, variable-metric updates, and multi-dimensional searches. The computational process for solving small and medium-size constrained optimization problems is usually based on unconstrained optimization. This provides a straightforward opportunity for the introduction of parallelism. In the present survey, however, we focus on promising approaches for solving large, well-structured constrained problems: dualization of problems with separable objective and constraint functions, and decomposition of hierarchical problems with linking variables (typical for Bender's decomposition in the linear case). Finally, we outline the key issues in future computational studies of parallel nonlinear optimization algorithms.

关键词： conjugate directions constrained optimization decomposition dual methods homogeneous functions multi-dimensional searches nonlinear programming parallel computing Unconstrained optimization variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

NEW LEAST-SQUARE ALGORITHMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1976年第2期18卷 187-197页

作者： DAVIDON, WC HAVERFORD COLL HAVERFORDPA 19041

New algorithms are presented for approximating the minimum of the sum of squares ofM real and differentiable functions over anN-dimensional space. These algorithms update estimates for the location of a minimum after each one of the functions and its first derivatives are evaluated, in contrast with other least-square algorithms which evaluate allM functions and their derivatives at one point before using any of this information to make an update. These new algorithms give estimates which fluctuate about a minimum rather than converging to it. For many least-square problems, they give an adequate approximation for the solution more quickly than do other algorithms.

关键词： gradient methods Least-square methods nonlinear programming variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

COMPUTATIONAL EXPERIENCE WITH DAVIDON LEAST-SQUARE ALGORITHM

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1980年第1期31卷 27-39页

作者： CORNWELL, LW KOCMAN, MG PROSSER, MF ANHEUSER BUSCH INC DEPT MANAGEMENT RESST LOUISMO 63118 BELL LABS DENVERCO

Computational results are presented for Davidon's new least-square algorithm. Computational experience with this algorithm is reported which motivated the development of a production code version of the algorithm. Several heuristic modifications, which have been added, are described. Fifteen zero-residual test problems have been used in comparing the new production code version with two established versions of the Levenberg-Marquardt algorithm. The production code version of Davidon's least-square algorithm performed faster and used less function evaluations than the Levenberg-Marquardt algorithm in almost every case of the test problems.

关键词： Least-square methods Levenberg-Marquardt methods nonlinear programming testing algorithms variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

DIRECT METHOD FOR GENERAL SOLUTION OF A SYSTEM OF LINEAR EQUATIONS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1975年第5-6期16卷 429-445页

作者： HUANG, HY RICE UNIV HOUSTONTX

A computationally stable method for the general solution of a system of linear equations is given. The system isA Tx−B=0, where then-vectorx is unknown and then×q matrixA and theq-vectorB are known. It is assumed that the matrixA T and the augmented matrix [A T,B] are of the same rankm, wherem≤n, so that the system is consistent and solvable. Whenm

关键词： computing methods conjugate-gradient methods linear equations Mathematical programming numerical methods variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

METHOD FOR DETERMINING EQUILIBRIUM STATES OF DYNAMIC-SYSTEMS

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第3期21卷 299-317页

作者： RED, WE UNIV SW LOUISIANA DEPT MECH ENGNLAFAYETTELA 70501

A heuristic method is presented for determining the equilibrium states of motion of dynamic systems, in particular, spacecraft. The method can also be applied to the solution of sets of linear or nonlinear algebraic equations. A positive-semidefinite functional is formed to convert the problem to that of finding those minimum points where the functional vanishes. The process is initiated within a selecteddomain of interest by random search; convergence to a minimum is obtained by a modified Davidon's deflected gradient technique. To render this approach feasible in the presence of constraints, the functional is modified to include penalty terms which cause the functional to approach infinity at the constraint boundaries. Close approximations to solutions near the constraint boundaries are found by applying Carroll's approach in successively reducing the weighting factors of the penalty terms. After finding a minimum, the local domain around this point is eliminated by adding to the functional an interior constraint term, representing the surface under a hypersphere centered at the minimum point. The domain of consideration now becomes the subdomain formed by subtracting the space contained within this hypersphere from the previous domain of interest. Minima are now sought within the remaining space, as before.

关键词： Aerospace engineering nonlinear programming penalty-function methods singular points variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

CLASS OF QUADRATICALLY CONVERGENT ALGORITHMS FOR CONSTRAINED FUNCTION MINIMIZATION

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1975年第5-6期16卷 447-485页

作者： HUANG, HY AGGARWAL, AK RICE UNIV DEPT MECH & AEROSP ENGN & MATHOUSTONTX

The problem of minimizing a functionf(x) subject to the constraint ϕ(x)=0 is considered. Here,f is a scalar,x is ann-vector, and ϕ is anm-vector, wherem

关键词： computing methods conjugate-gradient methods mathematical programming Nonlinear programming numerical methods quadratically convergent algorithms variable-metric methods

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：