Abstract
The present paper suggests a finite iteration technique for findinglocal minimum of a special type quasi-concave quadratic fractional functional subject to linear inequalities. The procedure adopted is exactly similar to “Simplex Technique” in linear programming and the problem has been attacked directly starting with a basic feasible solution and finding conditions under which the solution can be subjected to improvement. A numerical example has been given to illustrate the procedure.
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References
Aggarwal, S. P.: “A Simplex Technique for a particular Convex Programming Problem”. Canadian Operational Research Soc. Jour. Vol. 4, No. 2, pp. 82–89, 1966.
Bector, C. R.: “Programming problems with Convex Fractional Functions”. Opns. Res. (U.S.A.), Vol. 16, No. 2, 1968, pp. 383–391.
Candler, W. andR.J. Townsley: “The maximisation of a Quadratic function of variables subject to linear inequalities”. Management Science, Vol. 10, No. 3, 1964.
Charnes, A. andW. W. Cooper: “Programming with Linear Fractional Functionals”. Nav. Res. Log. Quart. Vol. 9, pp. 181–186 (Sept.–Dec. 1962).
Gass, S. I.: “Linear Programming”. McGraw-Hill, New York, 1958.
Gupta, S. K. andC. R. Bector: “Nature of Quotients, Products and Rational Powers of Convex (concave — Like Functions”. The Mathematics Student (India), 1968, pp. 63–67.
Hadley, G.: “Linear Programming”. Reading Mass: Addison Wesley, 1962.
Kanti, S.: “Quadratic Programming”. Cahiers du Centre d’Etudes de Recherche Operationelle, Vol. 8, No. 4, pp. 223–233, 1966.
Mangasarian, O. L.: “Pseudo Convex Functions”. J. SIAM Control, Ser. A., Vol. 3, No. 2, pp. 281–290, 1965.
Martos, B.: “The Direct Power of Adjacent Vertex Programming Methods”. Management Science, Vol. 12, No. 3, pp. 241–252, 1965.
Ponstein, J.: “Seven kinds of Convexity”. SIAM Review, Vol. 9, No. 1, pp. 115–120, 1967.
Rosen, J. B.: “The Gradient Projection Method for Non-linear Programming, Part I, Linear Constraints”. SIAM Jour. Vol. 8, pp. 181–217, 1960.
—— “The Gradient Projection Method for Non-linear Programming, Part II, Non-linear Constraints”. SIAM Jour. Vol. 9, pp. 514–532, 1961.
Zoutendijk, G.: “Maximising a Function in a Convex Region”. Jour. Roy. Stat. Soc. Ser. B. Vol. 21, pp. 338–355, 1959.
—— “Method of Feasible Directions”. Amsterdam: Elsevier, 1960.
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Bector, C.R. Indefinite quadratic fractional functional programming. Metrika 18, 21–30 (1972). https://doi.org/10.1007/BF02614233
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DOI: https://doi.org/10.1007/BF02614233