Abstract
This paper presents the design of the programme MINIFUN for solving non-linear optimization problems arising in research, development and engineering laboratories. The underlying algorithm is based on the penalty function approach whereby constrained optimization problems are solved via sequential unconstrained optimization. The paper shows the performance of several unconstrained optimization algorithms incorporated in MINIFUN, the significance of numerical differentiation, and finally a comparison of MINIFUN with other well-known programmes for non-linear optimization.
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References
J. Abadie and J. Guigou (1969). Gradient réduit généralisé. Note HI 069/02. Electricité de France, Paris.
E.M.L. Beale (1968). Matehmatical Programming in Practice. Pitman & Sons, London.
M.J. Box (1966). A comparison of several current optimization methods and the use of transformations in constrained problems. The Comp. J. 9, 67–77.
M.J. Box, D. Davies and W.H. Swann (1969). Nonlinear Optimization Techniques. Oliver & Boyd, London.
J. Bracken and G.P. McCormick (1968). Selected Applications of Nonlinear Programming. Wiley, New York.
C.G. Broyden (1970). The convergence of a class of double-rank minimization algorithms. 1. General considerations. J.I.M.A., 6, 76–90. 2. The new algorithm. J.I.M.A., 222–231.
W.C. Davidon (1959). Variable metric method for minimization. A.E.C. Research and Development Report ANL-5990.
A.V. Fiacco and G.P. McCormick (1968). Nonlinear Programming, Sequential Unconstrained Minimization Techniques. Wiley, New York.
R. Fletcher (1965). Function minimization without evaluating derivatives—review. The Comp. J., 8, 33–41.
R. Fletcher (1970). A new approach to variable metric algorithms. The Comp. J., 13, 317–322.
R. Fletcher and M.J.D. Powell (1963). A rapidly convergent descent method for minimization. The Comp. J., 6, 163–168.
R. Goffin, A. de Beer, A.C.M. Kilsdonk (1974). Non-linear Optimization Package OPTAC-II. Information Systems and Automation Department, N.V. Philips, Eindhoven.
J. Guigou (1971). Présentation et utilisation du code GREG. Note HI 582/2. Electricité de France, Paris.
R. Hooke and T.A. Jeeves (1961). Direct search solution of numerical and statistical problems. J.A.C.M. 8, 212–229.
J. Kowalik and M.R. Osborne (1968). Methods for Unconstrained Optimization Problems. American Elsevier, New York.
J.L. Kreuser and J.B. Rosen (1971). GPM/GPMNLC extended gradient projection method for non-linear constraints. University of Wisconsin, Madison.
F.A. Lootsma (1970). Boundary properties of penalty functions for constrained minimization. Philips Res. Repts. Suppl. 3.
F.A. Lottsma (1972a). Penalty function performance of several unconstrained minimization techniques. Philips Res. Repts. 27, 358–385.
F.A. Lootsma (1972b). A survey of methods for solving constrained-minimization problems via unconstrained minimization. In F.A. Lootsma (ed.), Numerical Methods for Non-Linear Optimization. Academic Press, London, 313–348.
F.A. Lootsma (1972c). The Algol 60 procedure minifun for solving non-linear optimization problems. Report 4761, Philips Research Laboratories, Eindhoven, the Netherlands.
G.P. McCormick, W.C. Mylander, and A.V. Fiacco (1965). Computer program implementing the sequential unconstrained minimization technique for nonlinear programming. Technical paper RAC-TP-151, Research Analysis Corporation, McLean, Virginia, USA.
J.A. Nelder and R. Mead (1964). A simplex method for function minimization. The Comp. J. 7, 308–313.
M.J.D. Powell (1964). An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Comp. J. 7, 155–162.
M.J.D. Powell (1970). A survey of numerical methods for unconstrained optimization. SIAM Review 12, 79–97.
M.J.D. Powell (1971). Recent advances in unconstrained optimization. Math. Progr. 1, 26–57.
R.W.H. Sargent (1973). Minimization without Constraints. In M. Avriet, M.J. Rijckaert and D.J. Wilde (eds.), Optimization and Design. Prentice-Hall, Englewood Cliffs, New Jersey, 37–75.
D.F. Shanno (1970). Conditioning of quasi-Newton Methods for function minimization. Math. of Comp. 24, 647–656.
R.L. Staha (1973). Constrained optimization via Moving Exterior Truncation. Thesis, University of Texas, Austin.
R.L. Staha and D.M. Himmelblau (1973). Evaluation of constrained nonlinear programming techniques. Working paper, University of Texas, Austin.
D. Tabak and B.C. Kuo (1971). Optimal Control by Mathematical Programming. Prentice-Hall, Englewood Cliffs, New Jersey.
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Lootsma, F.A. (1975). The design of a nonlinear optimization programme for solving technological problems. In: Bulirsch, R., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Mathematics, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079179
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DOI: https://doi.org/10.1007/BFb0079179
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