An external penalty-type method for multicriteria
An external penalty-type method for multicriteria
复制标题
一种多标准的外部惩罚型方法
DOI：
10.1007/s11750-015-0406-8
复制
发表时间：
2016
期刊：
影响因子：
1.7
通讯作者：
Luis M. Grana Drummond and Fernanda M. P. Raupp
中科院分区：
文献类型：
--
作者：
Ellen Hidemi Fukuda;Luis M. Grana Drummond and Fernanda M. P. Raupp
将经典的实值外部惩罚方法推广到多准则优化问题。作为它的单一目标对应物，它也需要一个外部惩罚函数来约束集，以及一个外生的非负实数发散序列，即所谓的惩罚参数，但是，与标量过程不同的是，矢量值方法使用一个辅助函数，该辅助函数可以在大量的“单调”实值映射中选择。分析了该类中辅助函数的性质，并举例说明。收敛结果与标量值方法相似，并且根据实现中使用的辅助函数的类型，在标准假设下，生成的不可行的序列收敛于弱Pareto或Pareto最优点。我们还提出了一种可实现的局部版本的外部惩罚方法，并研究了其收敛结果。
We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of “monotonic” real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method, and depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.