Geometric analysis of collaborative optimization

Xiang Li*, Weiji Li, Chang'an Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)

Abstract

Instead of the past mathematical analyses, an intuitive geometric analysis of the collaborative optimization (CO) algorithm is presented in this paper, which reveals some geometric properties of CO and gives a direct geometric interpretation of the reason for the reported computational difficulties in CO. The analysis shows that if the system-level optimum point at one iteration is outside the feasible region of the original optimization problem, at the next iteration, the system-level optimization problem may be infeasible due to the system-level consistency equality constraints. One way to solve the problem of the infeasibility is to relax the system-level consistency equality constraints using inequality constraints. However it is a delicate job to determine a rational relaxed tolerance because feasibility and consistency have conflicting requirements for the tolerance, that is, the more relaxed the better for feasibility while the stricter the better for consistency. Based on the geometric analysis, a method of variable relaxed tolerance is put forward to solve this problem. In this method, an adaptive adjustment of the tolerance is made at each iteration according to the quantified inconsistency between two subsystems. In the last section, the capabilities and limitations of the proposed method are illustrated by three examples.

Original languageEnglish
Pages (from-to)301-313
Number of pages13
JournalStructural and Multidisciplinary Optimization
Volume35
Issue number4
DOIs
Publication statusPublished - Apr 2008

Keywords

  • Collaborative optimization
  • Geometric analysis
  • Quantified inconsistency
  • Variable relaxed tolerance

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Li, X., Li, W., & Liu, C. (2008). Geometric analysis of collaborative optimization. Structural and Multidisciplinary Optimization, 35(4), 301-313. https://doi.org/10.1007/s00158-007-0127-1