Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as ADMM and PDHG can be learned and adapted. Case studies across LP, NNV, Sum-Rate maximization, OPF, and LRMP illustrate these gains.

翻译：大规模优化问题的求解需要兼具低单步计算开销的可扩展一阶方法。本教程聚焦优化领域的新范式：利用可微编程不仅执行算法，更学习如何设计算法。PyTorch、TensorFlow和JAX等现代框架通过高效自动微分技术支撑这一范式。将一阶方法嵌入此类系统可实现端到端训练，显著提升收敛效率与解质量。基于Fenchel-Rockafellar对偶理论，教程阐释了ADMM与PDHG等对偶驱动迭代框架的学习与自适应机制。线性规划、神经网络验证、和速率最大化、最优潮流及物流规划等典型案例验证了该方法的性能优势。