{"ID":2824052,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24295","arxiv_id":"2512.24295","title":"Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms","abstract":"When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For such methods, a lower per-iteration cost is advantageous when solving larger models. The contribution of this paper is two-fold. First, we propose a gradient-based algorithm with lower per-iteration cost than existing methods. Second, we further adapt this algorithm to exploit the piecewise-linear structure of neural networks that use Rectified Linear Units (ReLUs). In line with prior research, our methods become competitive with -- and then dominant over -- other local search methods as the optimization models become larger.","short_abstract":"When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solu...","url_abs":"https://arxiv.org/abs/2512.24295","url_pdf":"https://arxiv.org/pdf/2512.24295v2","authors":"[\"Jiatai Tong\",\"Yilin Zhu\",\"Thiago Serra\",\"Samuel Burer\"]","published":"2025-12-30T15:35:35Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}