Abstract
To date, the main emphasis in the development of numerical methods for solving semi-infinite programming problems has been on producing good locally convergent methods, and it seems that little attention has been given to the provision of globally convergent algorithms, except in some special cases. For many finite programming problems, good globally convergent methods based on the use of exact penalty functions are now available and it is the purpose of this paper to show that precisely analogous methods may be successfully used for a general class of semi-infinite programming problems.
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References
Clarke, F H: A new approach to Lagrange multipliers, Mathematics of Operations Research 1, 165–174 (1976).
Fahlander, K: Computer programs for semi-infinite optimization, TRITA-NA-7312 (Royal Institute of Technology, Sweden), (1973).
Fletcher, R: Numerical experiments with an exact L1 penalty function method, Nonlinear Programming 4, Proceedings of Madison Conference, 1980, eds. 0 L Mangasarian, R R Meyer, and S M Robinson (to appear).
Fletcher, R: Practical Methods of Optimization, Vol. II Constrained Optimization, John Wiley and Sons, Chichester (1981).
Gill, P E and W Murray: Newton-type methods for unconstrained and linearly constrained optimization, Math. Prog. 7, 311–350 (1974).
Gustafson, S-A and Koktanek: Numerical treatment of a class of semi-infinite programming problems, Nav. Res. Log. Quart. 20, 477–504 (1973).
Han, S P: A globally convergent method for nonlinear programming, J. of Opt. Th. and Appl. 22, 297–309 (1977).
Hettich, R: Ed. Semi-infinite Programming, Proceedings of a Workshop, Springer-Verlag, Berlin (1979).
Hettich, R and W Van Honstede: On quadratically convergent methods for semi-infinite programming, in [8], 97–111 (1979).
Honstede, W Van: An approximation method for semi-infinite problems, in [8], 126–136 (1979).
Powell, M J D: The convergence of variable metric methods for nonlinearly constrained optimization calculations, in Nonlinear Programming 3, eds. O L Mangasarian, R R Meyer and S M Robinson, Academic Press, New York (1978).
Powell, M J D: A fast algorithm for nonlinearly constrained optimization calculations, in Numerical Analysis, Dundee 1977, ed. G A Watson, Springer-Verlag, Berlin (1978).
Roleff, K: A stable multiple exchange algorithm for linear semi-infinite programming, in [8], 83–96 (1979).
Watson, G A: Globally convergent methods for semi-infinite programming, BIT 21, 362–373 (1981).
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Watson, G.A. (1983). Numerical Experiments with Globally Convergent Methods for Semi-Infinite Programming Problems. In: Fiacco, A.V., Kortanek, K.O. (eds) Semi-Infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46477-5_13
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DOI: https://doi.org/10.1007/978-3-642-46477-5_13
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