Sufficient optimality conditions for a separable product quasiconcave programming

In mathematical economics, the used functions are, in general, considered to be quasiconcave. Moreover, they are, in many cases, separable of nature. It is known that a local maximum of a quasiconcave function is not, in general, a global maximum. In this paper we will show that this property is true when the quasiconcave function is furthermore separable. Sufficient optimality conditions for a separable quasiconcave programming will be studied in both differentiable and nondifferentiable cases. Thanks to separability condition, quasiconcave functions have nice properties in optimization problems.