  In this paper, we investigate the relationships between proper efficiency and
the solutions of a general scalarization problem in multi-objective
optimization. We provide some conditions under which the solutions of the dealt
with scalar program are properly efficient and vice versa. We also show that,
under some conditions, if the considered general scalar problem is unbounded,
then the original multi-objective problem does not have any properly efficient
solution. In another part of the work, we investigate a general transformation
of the objective functions which preserves proper efficiency. We show that
several important results existing in the literature are direct consequences of
the results of the present paper.
