## 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].

### MSC:

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