NESC0556 KEELE

KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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1. NAME OR DESIGNATION OF PROGRAM: KEELE

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2. COMPUTERS

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Program name	Package id	Status	Status date
KEELE	NESC0556/01	Tested	01-JUN-1975

Machines used:

Package ID	Orig. computer	Test computer
NESC0556/01	IBM 370 series	IBM 370 series

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3. DESCRIPTION OF PROBLEM OR FUNCTION

KEELE is a linearly
constrained nonlinear programming algorithm for locating a local
minimum of a function of n variables with the variables subject to
linear equality and/or inequality constraints.

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4. METHOD OF SOLUTION

A variable metric procedure is used where the
direction of search  at each iteration is  obtained by multiplying
the negative of the gradient vector  by a positive definite matrix
which approximates  the inverse  of the  matrix of  second partial
derivatives associated with the function.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Array   dimensions
limit the number of variables to  20 and the number of constraints
to 50.  These can be changed by the user.

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6. TYPICAL RUNNING TIME

Total execution time for the four examples
in the report is approximately 10 seconds.

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7. UNUSUAL FEATURES OF THE PROGRAM

All input is through the
argument list and/or the common block /BAMRWH/.

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8. RELATED AND AUXILIARY PROGRAMS

This program is a modification of
the corresponding program described in reference 2.

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9. STATUS

Package ID	Status date	Status
NESC0556/01	01-JUN-1975	Tested at NEADB

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10. REFERENCES

G. W. Westley, A Linearly Constrained Nonlinear
Programming Algorithm, ORNL-4644, January 1971.
G. W. Westley and J. A. Watts, The Computing
Technology Center Numerical Analysis Library, CTC-39, 1970.

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11. MACHINE REQUIREMENTS: 31K bytes

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12. PROGRAMMING LANGUAGE(S) USED

Package ID	Computer language
NESC0556/01	FORTRAN-IV

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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED: OS/360.

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Three subroutines must be user-supplied. GRADNT defines the
gradient of the response surface, CONSTR defines the constraints
on the variables, and FVAL defines the response surface.

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15. NAME AND ESTABLISHMENT OF AUTHOR

                 G. W. Westley
                 Mathematics Division
                 Oak Ridge National Laboratory
                 P. O. Box X
                 Oak Ridge, Tennessee  37830

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16. MATERIAL AVAILABLE

NESC0556/01

File name	File description	Records
NESC0556_01.001	SOURCE PROGRAM USED FOR TESTING (F4)	1136
NESC0556_01.002	SUBROUTINE PACKAGE (F4)	1019
NESC0556_01.003	TEST PROGRAMS (F4)	117
NESC0556_01.004	SAMPLE PROBLEM PRINTED OUTPUT	359

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17. CATEGORIES

P. General Mathematical and Computing System Routines

Keywords: algorithms, iterative methods, nonlinear programming.