针对一类多目标优化问题的子梯度线性搜索技术

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-05-08 DOI:10.1007/s11117-024-01051-6

Dinesh Kumar, Geetanjali Panda

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引用次数: 0

摘要

本文提出了一种线性搜索技术，用于求解一类特殊的多目标优化问题，在这类问题中，目标函数应该是凸的，但不一定是可微分的。这是一个确定帕累托临界点的迭代过程。在迭代过程的每次迭代中，都会提出一个合适的子问题，利用该点上每个目标函数的次微分来确定方向向量。所提出的方法在数值实例中得到了验证。这种方法不像标量化方法那样需要选择合适的参数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A line search technique for a class of multi-objective optimization problems using subgradient

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A line search technique for a class of multi-objective optimization problems using subgradient

This paper proposes a line search technique to solve a special class of multi-objective optimization problems in which the objective functions are supposed to be convex but need not be differentiable. This is an iterative process to determine Pareto critical points. A suitable sub-problem is proposed at every iteration of the iterative process to determine the direction vector using the sub-differential of every objective function at that point. The proposed method is verified in numerical examples. This methodology does not bear any burden of selecting suitable parameters like the scalarization methods.

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.