Algorithm 734: A Fortran 90 code for unconstrained nonlinear minimization

ABSTRACT

This paper describes a Fortran 90 implementation of ACM Transactions on Mathematical Software Algorithm 630, a minimization algorithm designed for use in a limited-memory environment. It includes implementation of the Buckley-LeNir method, Nocedal's limited memory algorithm, and an experimental limited-memory implementation of a factored update due to Powell, as well as a fairly standard quasi-Newton implementation due originally to Shanno. This algorithm uses a number of the new features of Fortran 90 to offer capabilities that were not formerly available.

REFERENCES

• 1: A. G. Buckley, Conversion to Fortran 90: a case study, ACM Transactions on Mathematical Software (TOMS), v.20 n.3, p.308-353, Sept. 1994 [doi>10.1145/192115.192139]
• 2: BUCKLEY, A.G. 1989a. MinTest: A User's Guide. Tech. Rep. 1989CS-2, Dept. of Mathematics, Statistics and Computing Science, Dalhousie Univ., Halifax, Nova Scotia, Canada.
• 3: A. Buckley, Remark on algorithm 630, ACM Transactions on Mathematical Software (TOMS), v.15 n.3, p.262-274, Sept. 1989 [doi>10.1145/66888.69648]
• 4: BUC~.EY A.G.. 1989c. Test functions for unconstrained minimization. Tech. Rep. 1989CS-3, Dept of Mathematics, Statistics and Computing Science, Dalhousie Univ., Halifax~ Nova Scotia. Canada.
• 5: A. Buckley , A. Lenir, ALGORITHM 630: BBVSCG—a variable-storage algorithm for function minimization, ACM Transactions on Mathematical Software (TOMS), v.11 n.2, p.103-119, June 1985 [doi>10.1145/214392.214395]
• 6: J. C. Gilbert , C. Lemaréchal, Some numerical experiments with variable-storage quasi-Newton algorithms, Mathematical Programming: Series A and B, v.45 n.3, p.407-435, Dec. 1989 [doi>10.1007/BF01589113]
• 7: INTERNATIONAL STANDARDS ORGANIZATION. 1991. International standard ISO 1539: 1991. In Programmtng Language FORTRAN. International Standards Organization, New York.
• 8: LEE, A. 1993. Updating conjugate directions by the BFGS formula with variable storage. Master's thesis, Univ. of Victoria, Victoria, British Columbia, Canada.
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• 10: NOCEDAL, J. 1980. Updating quasi-Newton matrices with limited storage. Math. Comput. 35, 151 (July), 773-782.
• 11: M. J. D. Powell, Updating conjugate directions by the BRGS formula, Mathematical Programming: Series A and B, v.38 n.1, p.29-46, July 1, 1987 [doi>10.1007/BF02591850]
• 12: D. F. Shanno , K. H. Phua, Algorithm 500: Minimization of Unconstrained Multivariate Functions [E4], ACM Transactions on Mathematical Software (TOMS), v.2 n.1, p.87-94, March 1976 [doi>10.1145/355666.355673]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Gradient methods

General Terms:
Algorithms, Design

Keywords:
Fortran 90, conversion, limited memory, new features, nonlinear optimization, quasi-Newton