Fractional programming with invexity. (English) Zbl 0956.90051

Eberhard, Andrew (ed.) et al., Progress in optimization. Contributions from Australasia. 4th Optimization day, Melbourne, Australia, July 1997. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 30, 79-89 (1999).
Summary: Consider the nonlinear fractional programming problem: \[ \min_x f(x)/g(x) \quad\text{subject to}\quad h(x)\leq 0. \] Recently, Khan and Hanson gave sufficient conditions for optimality, and established duality results, assuming that \(f\) and \(-g\) are invex with respect to a scale function \(\eta(x,u)\), and \(h\) is invex with respect to \([g(u)/ g(x)] \eta(x,u)\). Here we show that the results hold if \(h\) is invex with respect to \(\eta(x,u)\), or to \(\beta(x,u) \eta(x,u)\) provided that \(\beta(x,u)\) is a positive scalar. Other duals are obtained under invex or quasiinvex hypotheses.
For the entire collection see [Zbl 0927.00033].


90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming