The paper presents a scalable learned iterative solver for nonlinear model predictive control (NMPC) that removes dependence on the prediction horizon by exploiting temporal decomposition in the network architecture. It introduces a closed‑loop resampling strategy to align training with deployment, achieving up to four‑fold speedups over IPOPT while maintaining comparable control performance and avoiding constraint violations. The method outperforms the previous monolithic LISCO approach on a CSTR cascade benchmark, scaling to larger problems without increasing network size.
By Lukas L\"uken, Sergio Lucia
The paper introduces “GraphPDHG,” a message‑passing neural network that aligns with the Chambolle‑Pock Primal–Dual Hybrid Gradient algorithm to solve general graph saddle‑point problems. The authors prove that “GraphPDHG” can efficiently simulate PDHG and can learn an accelerated version of the algorithm. Experiments demonstrate that the learned warm start improves second‑order optimizers and that alignment with PDHG yields better size generalization compared to standard GNN baselines.
By Samantha Chen, Jesse He, Coleman Clougherty, Gal Mishne, Chester Holtz
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.
By Lukas L\"uken, Sergio Lucia
Convex‑SKM‑Net is a neural layer that enforces convex constraints by constructing linearization halfspaces from residual and gradient oracles, avoiding constraint‑specific projections. It uses fixed‑depth dual projected‑gradient descent on GPU‑friendly matrix operations to solve minimum‑displacement block problems, jointly learning a predictor and a positive‑definite mobility matrix to shape corrections. The method converges theoretically, achieves sub‑$10^{-3}$ feasibility on SOC‑MPC and power‑system relaxations, and outperforms state‑of‑the‑art constraint‑satisfaction techniques with up to 144× speedups and near‑optimal objective gaps.
By Haoyu Zhu, Xiaochen Zhang, Qingchun Hou
The paper introduces SHSP, a Structure-Aware Hierarchical Solution Prediction framework for Mixed-Integer Linear Programming. SHSP replaces one-shot marginal decoding with a hierarchical conditional decoding that sequentially predicts variables based on a coupling graph derived from constraints, and includes a confidence-aware mask-and-repair step to correct errors. Experiments on four MILP benchmarks show SHSP reduces the solution gap by an average of 54% compared to existing one-shot methods.
By Zherong Zhang, Guanlin Li, Chengrui Gao, Haopu Shang, Ke Xue, Jixiang Lu, Weiyong Yang, Chao Qian
Mixed-Integer Linear Programming (MILP) is a fundamental optimization paradigm in combinatorial optimization and has been widely applied across real-world domains. Due to its NP-hard nature, obtaining...
The paper reports the first in‑space demonstration of using machine learning‑based warm starts to accelerate trajectory optimization for the Astrobee free‑flying robot on the International Space Station. A neural network is trained to learn the structure of the trajectory generation problem solved by sequential convex programming, and onboard predictions reduce solver iterations by 60% for rotational dynamics and 50% for obstacle‑laden scenarios. This approach enables real‑time trajectory planning while respecting safety constraints on limited flight hardware.
By Somrita Banerjee, Abhishek Cauligi, Marco Pavone
arXiv:2606. 00366v1 Announce Type: new Abstract: We consider the problem of generating a large collection of initial guesses for local minima of multimodal non-convex continuous optimization problems.
By Anjian Li, Bartolomeo Stellato, Ryne Beeson
arXiv:2607. 22467v1 Announce Type: new Abstract: Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve.
By Anjian Li, Ryne Beeson
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
By Trinh Tran, Binh Nguyen, Truong X. Nghiem
The paper introduces PolyFormer, a physics-informed machine learning framework that learns compact polytopic representations of complex constraints. By transforming constraint-induced geometry into efficient polytopic reformulations, PolyFormer reduces optimization complexity and enables the use of standard solvers. Evaluations on large‑scale resource aggregation, network‑constrained optimization, and uncertainty‑aware optimization show up to 6,400‑fold speedups and 99.87% memory savings while keeping feasibility and objective errors low.
By Yilin Wen, Yi Guo, Bo Zhao, Wei Qi, Zechun Hu, Colin Jones, Jian Sun
The paper introduces Sparse Sum-of-Squares (SOS) Layers, a new type of differentiable layer that reuses the sparse structure of forward semidefinite programming (SDP) solves during backpropagation. By avoiding dense certificate construction, the method achieves up to 2.7× faster warm‑call times and reduces memory usage from 160 GiB to 1.7 GiB on large problems. Experiments demonstrate its effectiveness across sparse polynomial certification, control, combinatorial relaxations, robotics, oscillator chains, and pose‑graph synchronization, achieving zero certified violations on unseen instances with far fewer optimization solves than finite‑difference approaches.
By Ege Gursoy, Nicolas Mansard