在无限维空间中确定近似固有效率

N. Hoseinpoor, M. Ghaznavi
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引用次数: 0

摘要

本文的主要思想是描述近似适当效率,这是多准则优化问题中广泛使用的最优性概念,可以防止解决方案具有无界权衡。分析了具有无穷多个目标函数问题的近似固有效率的一种修正。得到了这种近似固有效率修正的充分必要最优性条件。这种改进的近似保证了近似适当有效点作为加权和问题和改进的加权Tchebycheff范数问题的解的一般特征,即使存在无限个准则。所提供的关于修改定义的证明表明,如果目标函数的个数是无限的,那么在近似固有效率的原始定义下,这些结果是无效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Identifying approximate proper efficiency in an infinite dimensional space
The main idea of this article is to characterize approximate proper efficiency that is  a widely used optimality concept in multicriteria optimization problems that prevents  solutions having unbounded trade-offs. We analyze a modification of approximate proper  efficiency for problems with infinitely many objective functions. We obtain some necessary  and sufficient optimality conditions for this modification of approximate proper efficiency.  This modified version of approximation guarantees the general characterizations of approximate properly efficient points as solutions to weighted sum problems and modified  weighted Tchebycheff norm problems, even if there is an infinite number of criteria. The  provided proofs concerning the modified definition show that if the number of the objective  functions is infinite, then these results become invalid under the primary definition of  approximate proper efficiency.
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