TY - JOUR
T1 - Deep learning the efficient frontier of convex vector optimization problems
AU - Feinstein, Zachary
AU - Rudloff, Birgit
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/10
Y1 - 2024/10
N2 - 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.
AB - 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.
KW - Convex multi-objective optimization
KW - Convex vector optimization
KW - Deep learning
KW - Efficient frontier
KW - Machine learning
KW - Neural networks
UR - http://www.scopus.com/inward/record.url?scp=85194712769&partnerID=8YFLogxK
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U2 - 10.1007/s10898-024-01408-x
DO - 10.1007/s10898-024-01408-x
M3 - Article
AN - SCOPUS:85194712769
SN - 0925-5001
VL - 90
SP - 429
EP - 458
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 2
ER -