**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(alpha_{1},
alpha_{2},. . . 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.

**KEYWORD: ** OPTIMIZATION