Sufficient optimality conditions for a separable product quasiconcave programming

In mathematical economics, the widely used functions are, in general, considered to be quasiconcave, and they are, in many cases, separable of nature.However, it is known that a local maximum of a quasiconcave function is not, in general, a global maximum.Also, in the differentiable case, a critical point of a quasiconcave function is not necessarily a local maximum.In this paper, sufficient optimality conditions for a multiplicatively separable quasiconcave programming are studied in both unconstrained and inequality constrained cases, without differentiability assumption.Thanks to multiplicative separability condition, we show that quasiconcave functions have nice properties in optimization problems.