Conjugate Direction Methods in Optimization.pdf

Conjugate Direction Methods in Optimization

M. R. Hestenes

Shortly after the end of World War II high-speed digital computing machines were being developed. It was clear that the mathematical aspects of com­ putation needed to be reexamined in order to make efficient use of high-speed digital computers for mathematical computations. Accordingly, under the leadership of Min a Rees, John Curtiss, and others, an Institute for Numerical Analysis was set up at the University of California at Los Angeles under the sponsorship of the National Bureau of Standards. A similar institute was formed at the National Bureau of Standards in Washington, D. C. In 1949 J. Barkeley Rosser became Director of the group at UCLA for a period of two years. During this period we organized a seminar on the study of solu­ tions of simultaneous linear equations and on the determination of eigen­ values. G. Forsythe, W. Karush, C. Lanczos, T. Motzkin, L. J. Paige, and others attended this seminar. We discovered, for example, that even Gaus­ sian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed. During this period Lanczos developed his three-term relationship and I had the good fortune of suggesting the method of conjugate gradients. We dis­ covered afterward that the basic ideas underlying the two procedures are essentially the same. The concept of conjugacy was not new to me. In a joint paper with G. D.

26.07.2000 · Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. Conjugate Direction Methods in Optimization - M. …

9.84 MB DATEIGRÖSSE
1461260507 ISBN
Englisch SPRACHE
Conjugate Direction Methods in Optimization.pdf

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Chapter 10 Conjugate Direction Methods An Introduction to Optimization Spring, 2012 Wei-Ta Chu 1 2012/4/13. Introduction Conjugate direction methods can be viewed as being intermediate between the method of steepest descent and Newton’s method. Solve quadratics of variables in steps. The usual implementation, the conjugate gradient algorithm, requires no Hessian matrix evaluations. No matrix Optimization Method - an overview | …

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20.11.2019 · In this paper, we present a new conjugate gradient method using an acceleration scheme for solving large-scale unconstrained optimization. The generated search direction satisfies both the sufficient descent condition and the Dai–Liao conjugacy condition independent of line search. Moreover, the value of the parameter contains more useful information without adding more computational cost