On constructing total orders and solving vectoroptimization problems with total orders

摘要

In this paper, we introduce a construction method of total ordering cone on R~n.It is shown that any total ordering cone on R~n is isomorphic to the cone R~n_lex. Existence ofa total ordering cone that contain given cone with a compact base is shown. By using thiscone, a solving method of vector and set valued optimization problems is presented.