# VARIABLE METRIC METHOD FOR MINIMIZATION

## Abstract

A method for determining numerically local minima of differentiable functions of several variables is presented. In the process of locating each minimum, a matrix which characterizes the behavior of the iunction about the minimum is determined. For a region in which the function depends quadratically on the variables, no more than N iterations are required, where N is the number of variables. By suitable choice of starting values and without modification of the procedure, linear constraints can be imposed upon the variables. (auth)

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., Lemont, Ill.

- OSTI Identifier:
- 4222000

- Report Number(s):
- ANL-5990(Rev.)

- NSA Number:
- NSA-14-004491

- DOE Contract Number:
- W-31-109-ENG-38

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-60

- Country of Publication:
- United States

- Language:
- English

- Subject:
- MATHEMATICS AND COMPUTERS; DIFFERENTIAL EQUATIONS; MATHEMATICS; MATRICES; NUMERICALS

### Citation Formats

```
Davidon, W.C.
```*VARIABLE METRIC METHOD FOR MINIMIZATION*. United States: N. p., 1959.
Web. doi:10.2172/4222000.

```
Davidon, W.C.
```*VARIABLE METRIC METHOD FOR MINIMIZATION*. United States. doi:10.2172/4222000.

```
Davidon, W.C. Sun .
"VARIABLE METRIC METHOD FOR MINIMIZATION". United States. doi:10.2172/4222000. https://www.osti.gov/servlets/purl/4222000.
```

```
@article{osti_4222000,
```

title = {VARIABLE METRIC METHOD FOR MINIMIZATION},

author = {Davidon, W.C.},

abstractNote = {A method for determining numerically local minima of differentiable functions of several variables is presented. In the process of locating each minimum, a matrix which characterizes the behavior of the iunction about the minimum is determined. For a region in which the function depends quadratically on the variables, no more than N iterations are required, where N is the number of variables. By suitable choice of starting values and without modification of the procedure, linear constraints can be imposed upon the variables. (auth)},

doi = {10.2172/4222000},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1959},

month = {11}

}

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