Weak efficiency in multiobjective equasicon vex optimization on the real-line without derivatives

Abstract

This paper deals with the problem of existence of weakly efficient solution to quasiconvex vector optimization problems in a finite dimensional setting on the real-line. This consideration is motivated by algorithmic purp oses, because it is expected that, like in scalar minimization, one must solve a one-dimensional problem to and the next iterate. We start by recalling a notion of nonconvexit y weak er than quasicon vexit y for vector functions introduced ealier by one of the author in an previous paper. After wards, we characterize the nonemptiness and/or compactness of the weakly efficient solution set. Then, this set is described as much as possible in the multiobjective case, and the bicriteria problem is carefully analized when each component is lower semicontinuous and quasicon vex. Several examples showing the applicabilit y of our results are presented, and various algorithms are stated to compute the overall weakly efficient solutionse.