A Duality Theorem for a Nondifferentiable Fractional Programming Problem

Abstract

A fractional analogue of Sinha's problem [Sinha, S. M. 1966. A duality theorem for nonlinear programming. Management Sci. 12 385.] is considered and duality theory is developed for it. This duality subsumes duality results of Chadha [Chadha, S. S. 1971. A dual fractional program. ZAMM 51 560.] and Sinha [Sinha, S. M. 1966. A duality theorem for nonlinear programming. Management Sci. 12 385.], and gives a dual to the minimum risk problem of stochastic programming studied by Bergthaller [Bergthaller, C. 1970. A quadratic equivalent of the minimum risk problem. Revue Roumaine Math. pur. appl. 15 17.].