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Infinite non-linear programming

Published online by Cambridge University Press:  09 April 2009

M. A. Hanson
M. A. Hanson
Affiliation:
Department of Statistics, University of New South WalesSydney.
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In recent years there has been extensive development in the theory and techniques of mathematical programming in finite spaces. It would be very useful in practice to extend this development to infinite spaces, in order to treat more realistically the problems that arise for example in economic situations involving infinitely divisible processes, and in particular problems involving time as a continuous variable. A more mathematical reason for seeking such generalisation is possibly that of obtaining a unification mathematical programming with other branches of mathematics concerned with extrema, such as the calculus of variations.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 3 , August 1963 , pp. 294 - 300
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Duffin, R. J., “Infinite Programs”, Linear Inequalities and Related Systems, Princeton University Press, 1956.Google Scholar
[2]Hurwicz, L., “Programming in Linear Spaces”, Studies in Linear and Non-Linear Programming, Stanford University Press, California, 1958.Google Scholar
[3]Kuhn, H. W. and Tucker, A. W., “Non-linear programming”, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability University of California Press, 1951.Google Scholar
[4]Karlin, S., “Mathematical Methods and Theory in Games, Programming and Economics”, Addison-Wesley Publ. Co., Inc., Mass., 1959.Google Scholar
[5]Dennis, J. B., “Mathematical Programming and Electrical Networks”, Technology Press and John Wiley and Sons, New York, 1959.Google Scholar
[6]Dorn, W. S., “Duality in Quadratic Programming”, Q. Appl. Math., 18, 155–162, 07 1960.Google Scholar
[7]Dorn, W. S., “A Duality Theorem for Convex Programs”, I.B.M. Journal, 4, 407–413, 10 1960.Google Scholar
[8]Wolfe, P., “A Duality Theorem for Non-linear Programming”, Q. Appl. Math., 19, 239–244, 1961.Google Scholar
[9]Hanson, M. A., “A Duality Theorem in Non-linear Programming with Non-linear Constraints”, Austral. J. Statistics, 3, 64–72, 1961.Google Scholar