Input convex neural networks as surrogates in mathematical optimisation
Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research. The prevailing approach uses feedforward neural networks (FNNs) with ReLU activations, whose piecewise-linear structure admits an exact but computationally intensive mixed-integer programming (MIP) reformulation as the networks grow. We advocate input convex neural networks (ICNNs) as structurally superior surrogates when the underlying response is approximately convex or concave. The convex architecture offers two computational advantages. First, the ICNN-MIP formulation tends to yield a tighter linear programming (LP) relaxation than its FNN-MIP counterpart, wi...
| Authors | Yu Liu, Jan Kronqvist, Fabricio Oliveira |
|---|---|
| Primary category | math.OC |
| Published | 10 August 2026 |
| Last updated at source | 10 August 2026 |
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