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NESC0753 OCOPTR,DRVOCR

OCOPTR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation
DRVOCR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation

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1. NAME OR DESIGNATION OF PROGRAM:  OCOPTR,DRVOCR
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2. COMPUTERS
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Program name Package id Status Status date
OCOPTR NESC0753/01 Tested 01-OCT-1979

Machines used:

Package ID Orig. computer Test computer
NESC0753/01 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

OCOPTR and DRVOCR are computer  programs designed to find minima of non-linear differentiable functions f: R**n--->R with n dimensional domains.
OCOPTR requires that the user only provide function values (i.e. it  is a derivative-free routine). DRVOCR requires the user to supply both function and gradient information.
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4. METHOD OF SOLUTION

OCOPTR and DRVOCR use the variable metric (or quasi-Newton) method of Davidon (1975). For OCOPTR, the derivatives  are estimated by finite differences along a suitable set of linearly independent directions. For DRVOCR, the derivatives are user- supplied. Some features of the codes are the storage of the approximation to the inverse Hessian matrix in lower trapezoidal factored form and the use of an optimally-conditioned updating method. Linear equality constraints are permitted subject to the initial Hessian factor being chosen correctly.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The functions to which the routine is applied are assumed to be differentiable. The routine also requires (n**2/2) + 0(n) storage locations where n is the problem dimension.
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6. TYPICAL RUNNING TIME

Running time is problem-dependent. The NESC executed the sample problems in 6 CPU seconds for both programs on an IBM370/195.
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS:
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9. STATUS
Package ID Status date Status
NESC0753/01 01-OCT-1979 Tested at NEADB
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10. REFERENCES

- W.C. Davidon:
  Optimally Conditioned Optimization Algorithms without Line
  Searches
  Mathematical Programming, Vol. 9, pp. 1-30, 1975.
NESC0753/01, included references:
- W.C. Davidon, L. Nazareth:
  OCOPTR - A Derivative Free FORTRAN Implementaion of Davidon's
  Optimally Conditioned Method
  TM-303 (August 1977).
- W.C. Davidon, L. Nazareth:
  DRVOCR - A FORTRAN Implementaion of Davidon's Optimally
  Conditioned Method
  TM-306 (August 1977).
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11. MACHINE REQUIREMENTS:  50K of memory is required.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0753/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   OS/MVT.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

                 J. L. Nazareth
                 Applied Mathematics Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
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16. MATERIAL AVAILABLE
NESC0753/01
File name File description Records
NESC0753_01.001 OCOPTR (DRV. FREE ROUTINE) SOURCE (F4) 1274
NESC0753_01.002 OCOPTR USER'S ROUTINE (F4,EBCDIC) 130
NESC0753_01.003 OCOPTR SAMPLE OUTPUT 99
NESC0753_01.004 DRVOCR (DRV. ROUTINE) SOURCE (F4,EBCDIC) 1236
NESC0753_01.005 DRVOCR USER'S ROUTINE (F4,EBCDIC) 134
NESC0753_01.006 DRVOCR SAMPLE OUTPUT 96
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: finite difference method, nonlinear problems, optimization.