Sufficient optimality conditions for a separable product quasiconcave programming

TL;DR

This paper establishes sufficient optimality conditions for separable quasiconcave programming, highlighting that local maxima are also global maxima under separability, with implications for economic optimization problems.

Contribution

It provides new sufficient optimality conditions for separable quasiconcave functions, extending understanding in both differentiable and nondifferentiable cases.

Findings

Local maxima are global for separable quasiconcave functions

Optimality conditions are derived for differentiable cases

Optimality conditions are extended to nondifferentiable cases

Abstract

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.