A proximal method for multiobjective quasiconvex minimization on the nonnegative orthant and its application to demand theory in microeconomy

Abstract

ABSTRACT In this paper we propose an inexact proximal point method to solve multiobjective minimization problems with locally Lipschitz quasiconvex objective functions on the nonnegative orthant. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we obtain the convergence of the sequences generated by the algorithm. We give some computational results and an application to demand theory is presented.