Deep learning the efficient frontier of convex vector optimization problems

Zachary Feinstein () and Birgit Rudloff ()
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Zachary Feinstein: Stevens Institute of Technology
Birgit Rudloff: Vienna University of Economics and Business

Journal of Global Optimization, 2024, vol. 90, issue 2, No 6, 429-458

Abstract: 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.

Keywords: Convex vector optimization; Convex multi-objective optimization; Machine learning; Deep learning; Neural networks; Efficient frontier (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01408-x

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