NESC0922 VMCON.

1. NAME OR DESIGNATION OF PROGRAM:  VMCON.

3. DESCRIPTION OF PROBLEM OR FUNCTION

VMCON minimizes a nonlinear function subject to nonlinear equality and inequality constraints.

4. METHOD OF SOLUTION

VMCON uses an iterative quadratic programming method with a quasi-Newton estimate of the Hessian of the Lagrangian to generate new solution estimates.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

6. TYPICAL RUNNING TIME

Compilation and execution of the sample problems takes 39 CPU seconds on an IBM370/195. Execution required 7.5 CPU seconds. NESC executed the sample problems in less than 1 second of CPU time on an IBM3033.

7. UNUSUAL FEATURES OF THE PROGRAM

The approach used in VMCON requires significantly fewer function evaluations than are required  by penalty, augmented Lagrangian, or projection techniques.

8. RELATED AND AUXILIARY PROGRAMS

VMCON uses modifications of the United Kingdom Atomic Energy Authority's Harwell Subroutine Library  routines VE02AD and LA02AD, routines from MINPACK1 (NESC Abstract 888), LINPACK (NESC Abstract 800), and several of the Basic Linear Algebra Subprograms (BLAS). All of the required routines are included in the package.

10. REFERENCES

- Chuck L. Lawson, Richard J. Hanson, David R. Kincaid, and Fred T.
  Krough,
  Basic Linear Algebra Subprograms for FORTRAN Usage,
  SAND77-0898, October 1977 (also published in Association for
  Computing Machinery, Transactions on Mathematical Software,
  Vol. 5, No. 3, pp. 308-323, September 1979).
- M.J.D. Powell,
  Algorithms for Nonlinear Constraints That Use Lagrangian
  Functions, Mathematical Programming, Vol. 14, pp. 224-248, 1978.
- M.J.D. Powell,
  "A Fast Algorithm for Nonlinearly Constrained Optimization
Calculations", in Lecture Notes in Mathematics, Numerical Analysis    Proceedings, Biennial Conference, Dundee 1977, Vol. 630, pp.
  144-157, A. Dodd and B. Eckmann, Eds., Springer-Verlag, New York,
  Heidelberg, Berlin, 1978.
- VMCON, NESC No. 922.370, VMCON Tape Description, National Energy
  Software Center Note 81-29, March 23, 1981.

- R.L. Crane, K.E. Hillstrom and M. Minkoff:
  Solution of the General Nonlinear Programming Problem with
  Subroutine VMCON.  ANL-80-64 (July 1980).

11. MACHINE REQUIREMENTS

95K bytes of memory are required to execute VMCON with the sample problems provided.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/370.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The
FORTRAN IV G1 or H-Extended Compiler must be used to compile the sample driver provided because of the list-directed READ statements. Subroutine FCN which calculates the objective function and constraint functions must be supplied by the user.

15. NAME AND ESTABLISHMENT OF AUTHOR

             K.E. Hillstrom and M. Minkoff*
             Applied Mathematics Division
             Argonne National Laboratory
             9700 South Cass Avenue
             Argonne, Illinois 60439

             R.L. Crane
             RCA David Sarnoff Research Center
             Princeton, New Jersey 08540
* Contact

File name	File description	Records
NESC0922_01.002	VMCON INFORMATION	24
NESC0922_01.003	VMCON, MAIN PROGRAM SOURCE (FORTRAN-4)	110
NESC0922_01.004	VMCON, SUBROUTINES SOURCE (FORTRAN-4)	2363
NESC0922_01.005	FCN SUBROUTINE FOR TEST CASE 1 (FORTRAN-4)	34
NESC0922_01.006	VMCON, JCL FOR TEST CASE 1	10
NESC0922_01.007	VMCON, INPUT FOR TEST CASE 1	6
NESC0922_01.008	VMCON, OUTPUT OF TEST CASE 1	232
NESC0922_01.009	FCN SUBROUTINE FOR TEST CASE 2 (FORTRAN-4)	34
NESC0922_01.010	VMCON, JCL FOR TEST CASE 2	10
NESC0922_01.011	VMCON, INPUT FOR TEST CASE 2	2
NESC0922_01.012	VMCON, OUTPUT OF TEST CASE 2	66