Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff Topological Vector Spaces

摘要

Piecewise linear vector optimization problems in a locally convex Hausdorfftopological vector spaces setting are considered in this paper. The efficientsolution set of these problems are shown to be the unions of finitely manysemi-closed generalized polyhedral convex sets. If, in addition, the problem isconvex, then the efficient solution set and the weakly efficient solution setare the unions of finitely many generalized polyhedral convex sets and they areconnected by line segments. Our results develop the preceding ones of Zheng andYang [Sci. China Ser. A. 51, 1243--1256 (2008)], and Yang and Yen [J. Optim.Theory Appl. 147, 113--124 (2010)], which were established in a normed spacessetting.