Vector optimization using improvement sets in locally convex spaces

This paper aims to study vector optimization through improvement sets in locally convex spaces. This investigation could be viewed as an extension of the work of Lalitha and Chatterjee (J Optim Theory Appl 166: 825–843, 2015) who studied an open problem on stability posed by Chicco et al., in normed linear spaces. This paper also establishes some existence results for this kind of vector optimization using the celebrated KKM theorem (or Fan’s Lemma, which is more common in the literature). Some examples illustrating the advantage of this work than that of Lalitha and Chatterjee (2015) are included too.