最优化与控制：2025–2026 年度综述

An annual survey of the math.OC arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 100 papers and organised into 20 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• Robust and Distributed Control of Complex Dynamic Systems (81.4%) — Focuses on robust optimization, distributed control, and adaptive strategies for complex systems including multi-agent consensus, hybrid dynamics, and transportation networks under uncertainty and communication constraints.
• Convex and Stochastic Optimization with Structural Constraints (13.3%) — Addresses algorithmic design and theoretical analysis for convex, linearly constrained, and stochastic optimization problems, including bilevel optimization and spectral methods for optimal control.
• Gradient Flow Dynamics and Convergence Analysis (2.1%) — Investigates the convergence properties and global behavior of gradient-based optimization algorithms, including mirror descent, control-based Lagrangian flows, and particle gradient methods.
• Reinforcement Learning and Deep Learning Integration (1.4%) — Explores the intersection of machine learning and control theory, specifically focusing on deep reinforcement learning, continuous-time RL, and neural network-based optimization frameworks.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.