ABSTRACT

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.

摘要

在本文中，我们研究了适当效率与多目标优化中一般标量化问题的解决方案之间的关系。我们提供了一些条件，在这些条件下，处理的标量程序的解决方案是适当有效的，反之亦然。我们还表明，在某些情况下，如果所考虑的一般标量问题是无界的，则原始多目标问题没有任何适当有效的解决方案。在工作的另一部分，我们研究了保持适当效率的目标函数的一般转换。我们表明，文献中存在的几个重要结果是本文结果的直接结果。