Deep learning the efficient frontier of convex vector optimization problems

Zachary Feinstein, Birgit Rudloff

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater’s condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.

Original languageEnglish
Pages (from-to)429-458
Number of pages30
JournalJournal of Global Optimization
Volume90
Issue number2
DOIs
StatePublished - Oct 2024

Keywords

  • Convex multi-objective optimization
  • Convex vector optimization
  • Deep learning
  • Efficient frontier
  • Machine learning
  • Neural networks

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