RSIC COMPUTER CODE PSR-001

1. NAME AND TITLE

MAX-XTREME: Generalized Several-Constraint LaGrange Multiplier.

2. CONTRIBUTOR

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

3. CODING LANGUAGE AND COMPUTER

Fortran 63; CDC 1604.

4. NATURE OF PROBLEM SOLVED

MAX was written to solve the one-constraint LaGrange multiplier problem; XTREME is MAX expanded to solve the problem with several constraints.

The method of LaGrange multipliers seeks to find a stationary value for some function W = W(alpha₁, alpha₂,. . . alpha_J), subject to constraints which take the form of equality conditions.

5. METHOD OF SOLUTION

Numerical methods are used to solve the LaGrange multiplier problem. XTREME deals with up to 25 independent variables. It finds an extreme value for an object function subject to a number of equality constraints, at most one less than the number of independent variables. All second derivatives of the object function must exist everywhere in the domain of computation.

6. RESTRICTIONS OR LIMITATIONS

None noted.

7. TYPICAL RUNNING TIME

No study has been made by RSIC of typical running times for MAX-TREME.

8. COMPUTER HARDWARE REQUIREMENTS

MAX-TREME was designed for the CDC 1604 computer.

9. COMPUTER SOFTWARE REQUIREMENTS

MAX-TREME was written in Fortran 63 to run on the COOP Monitor System.

10. REFERENCES

F. H. S. Clark and F. B. K. Kam, "A Generalized One-Constraint LaGrange Multiplier Numerical Formulation," ORNL-3742 (March 1965).

F. B. K. Kam and F. H. S. Clark, "Numerical Solution of the LaGrange Multiplier Problem with Several Constraints," ORNL-3846 (December 1965).

11. CONTENTS OF CODE PACKAGE

Included are the referenced documents and one (1.2MB) DOS diskette.

12. DATE OF ABSTRACT

November 1972.