A two-point heuristic to calculate the stepsize in subgradient method with application to a network design problem

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization Pub Date : 2024-01-01 DOI:10.1016/j.ejco.2024.100092

F. Carrabs , M. Gaudioso , G. Miglionico

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引用次数: 0

Abstract

We introduce a heuristic rule for calculating the stepsize in the subgradient method for unconstrained convex nonsmooth optimization which, unlike the classic approach, is based on retaining some information from previous iteration. The rule is inspired by the well known two-point stepsize by Barzilai and Borwein (BB) [6] for smooth optimization and it coincides with (BB) in case the function to be minimised is convex quadratic.

Under the use of appropriate safeguards we demonstrate that the method terminates at a point that satisfies an approximate optimality condition.

The proposed approach is tested in the framework of Lagrangian relaxation for integer linear programming where the Lagrangian dual requires maximization of a concave and nonsmooth (piecewise affine) function. In particular we focus on the relaxation of the Minimum Spanning Tree problem with Conflicting Edge Pairs (MSTC). Comparison with classic subgradient method is presented. The results on some widely used academic test problems are provided too.

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计算子梯度法步长的两点启发式，并应用于网络设计问题

我们引入了一种启发式规则，用于计算无约束凸非光滑优化子梯度法中的步长，与传统方法不同的是，该规则基于保留前一次迭代的某些信息。该规则的灵感来自 Barzilai 和 Borwein (BB) [6]针对平滑优化提出的众所周知的两点步长，并且在需要最小化的函数为凸二次函数的情况下与 (BB) 不谋而合。我们尤其关注有冲突边对的最小生成树问题（MSTC）的松弛。与经典的子梯度法进行了比较。此外，我们还提供了一些广泛使用的学术测试问题的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

EURO Journal on Computational Optimization OPERATIONS RESEARCH & MANAGEMENT SCIENCE-

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

60 days

期刊介绍： The aim of this journal is to contribute to the many areas in which Operations Research and Computer Science are tightly connected with each other. More precisely, the common element in all contributions to this journal is the use of computers for the solution of optimization problems. Both methodological contributions and innovative applications are considered, but validation through convincing computational experiments is desirable. The journal publishes three types of articles (i) research articles, (ii) tutorials, and (iii) surveys. A research article presents original methodological contributions. A tutorial provides an introduction to an advanced topic designed to ease the use of the relevant methodology. A survey provides a wide overview of a given subject by summarizing and organizing research results.