Haizhou Liu, Lun Yang, Xinwei Shen, Qinglai Guo, Hongbin Sun, Mohammad Shahidehpour
In this letter, we propose a data-driven warm start approach, empowered by artificial neural networks, to boost the efficiency of convex relaxations in optimal gas flow. Case studies show that this approach significantly decreases the number of iterations for the convex-concave procedure algorithm, and optimality and feasibility of the solution can still be guaranteed.
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In hybrid Model Predictive Control (MPC), a Mixed-Integer Quadratic Program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect consecutive problem instances to be nearly identical. This paper addresses the question of how computations performed at one time step can be reused to accelerate (warm start) the solution of subsequent MIQPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branch-and-bound algorithm allows an efficient r…
We consider warm-started optimized trajectory planning for autonomous surface vehicles (ASVs) by combining the advantages of two types of planners: an A* implementation that quickly finds the shortest piecewise linear path, and an optimal control-based trajectory planner. A nonlinear 3-degree-of-freedom underactuated model of an ASV is considered, along with an objective functional that promotes energy-efficient and readily observable maneuvers. The A* algorithm is guaranteed to find the shortest piecewise linear path to the goal position based on a uniformly decomposed map. Dynamic informatio…
Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF
提出一种线性割平面松弛方法，利用外包络线性割和现代割管理技术，快速求解ACOPF紧致下界，并证明在数据变化场景下割可有效热启动算法。
A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished…
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing resources, this paper proposes a few approaches to solving MIQPs, either to optimality or suboptimally. We specialize an existing Accelerated Dual Gradient Projection (GPAD) algorithm to effectively solve the Quadratic Programming (QP) relaxation that arise during Branch and Bound (B&B) and propose a generic framework to warm-start the binary variables which redu…
A New Duality-Free Framework for Convex Optimisation with Superlinear Convergence and Effective Warm-Starting
本文提出了一种无对偶框架，用于凸优化问题，实现了超线性收敛和有效的预热启动，通过数值实验展示了其在MPC问题中的优越性能。
Learning to Warm-Start Fixed-Point Optimization Algorithms
提出一种机器学习框架，通过神经网络预测热启动来加速不动点优化算法，并提供了PAC-Bayes泛化界，实验证明能显著减少迭代次数和求解时间。
First-order methods are widely used to solve convex quadratic programs (QPs) in real-time applications because of their low per-iteration cost. However, they can suffer from slow convergence to accurate solutions. In this paper, we present a framework which learns an effective warm-start for a popular first-order method in real-time applications, Douglas-Rachford (DR) splitting, across a family of parametric QPs. This framework consists of two modules: a feedforward neural network block, which takes as input the parameters of the QP and outputs a warm-start, and a block which performs a fixed …
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the objective function, vary only marginally from one time step to the next. In this case, recomputing the optimal solution at each time represents a significant burden for real-time applications. This paper proposes a novel algorithm to approximately solve a perturbed constrained dynamic program that significantly improves the computational burden when the obje…
LOTUS: A Warm-Start Framework for Powering Dual Decomposition in Large-Scale Two-Stage Stochastic Programs
LOTUS通过子集启动框架提升双分解在大型两阶段随机规划中的效率，实现更快的原问题收敛和更优的解质量。
We present Newton-Krylov methods for efficient numerical solution of optimal control problems arising in model predictive control, where the optimal control is discontinuous. As in our earlier work, preconditioned GMRES practically results in an optimal $O(N)$ complexity, where $N$ is a discrete horizon length. Effects of a warm-start, shifting along the predictive horizon, are numerically investigated. The~method is tested on a classical double integrator example of a minimum-time problem with a known bang-bang optimal control.
Warm-Started QAOA with Custom Mixers Provably Converges and Computationally Beats Goemans-Williamson's Max-Cut at Low Circuit Depths
提出 QAOA-warmest，用半定规划随机投影热启动与自定义混合器初始化 QAOA，证明其绝热收敛，并在低深度模拟及真实硬件上优于标准 QAOA 和 Goemans-Williamson。
Sequential Convex Programming with Filtering-Based Warm-Starting for Continuous-Time Multiagent Quadrotor Trajectory Optimization
针对多四旋翼连续时间轨迹优化中离散点间约束违反及迭代求解收敛慢问题，提出结合序列凸规划与滤波预热启动的框架，通过转化约束、贝叶斯近似预热加速收敛，实现全轨迹约束满足且计算时间减少两个数量级。
Warm-starting outer approximation for parameterized convex MINLP
针对参数化凸混合整数非线性规划序列，提出基于外逼近的热启动技术，理论证明在参数线性依赖下可单次迭代收敛，数值实验显示显著加速。
Policy Optimization for PDE Control with a Warm Start
针对非线性PDE降阶建模误差导致控制器性能下降的问题，提出以基于模型的控制器为热启动并加入策略优化微调的“先降维、再设计、后适应”方法，少量迭代即可显著提升跟踪控制性能。
Solving General QUBOs with Warm-Start QAOA via a Reduction to Max-Cut
本文研究如何将基于最大割SDP松弛的QAOA热启动方法通过标准归约推广到一般QUBO问题，并与直接QUBO松弛方法进行实验比较，发现最佳热启动策略取决于具体问题类型。
Warm-IP: A Path-Following ADMM Warm Start for Interior-Point Quadratic Programming
Warm-IP是结合ADMM路径追踪变体与原始-对偶IP方法的混合框架，在含60例肺癌的大规模放疗QP基准上，其求解速度与稳定性均显著优于MOSEK、Gurobi等现有求解器。
Theoretical Approximation Ratios for Warm-Started QAOA on 3-Regular Max-Cut Instances at Depth $p=1$
本文推广了 Farhi 等人的技术，为 3-正则最大割实例上暖启动 QAOA 建立了近似比下界，并通过分析初始化角度与经典割编码比特串的影响，证明不存在能同时超越标准 QAOA 和经典算法的初始化角度，同时发现 60° 可有效恢复暖启动割。
In this paper, we propose a framework to build a memory of motion for warm-starting an optimal control solver for the locomotion task of a humanoid robot. We use HPP Loco3D, a versatile locomotion planner, to generate offline a set of dynamically consistent whole-body trajectory to be stored as the memory of motion. The learning problem is formulated as a regression problem to predict a single-step motion given the desired contact locations, which is used as a building block for producing multi-step motions. The predicted motion is then used as a warm-start for the fast optimal control solver …
A large amount of data has been generated by grid operators solving AC optimal power flow (ACOPF) throughout the years, and we explore how leveraging this data can be used to help solve future ACOPF problems. We use this data to train a Random Forest to predict solutions of future ACOPF problems. To preserve correlations and relationships between predicted variables, we utilize a multi-target approach to learn approximate voltage and generation solutions to ACOPF problems directly by only using network loads, without the knowledge of other network parameters or the system topology. We explore …
WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers
本文提出 WARP 基准测试，用于评估内点法的 primal-dual 预热方法。通过对比传统预热方法，发现仅使用 primal 预热无法有效减少迭代次数，而采用 full primal-dual-barrier 状态可显著降低迭代次数。
Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketching
针对大规模半定规划求解慢且难以利用热启动的问题，提出带草图化的统一谱捆绑（USBS）算法，在保持收敛速度的同时实现高可扩展性，并支持热启动加速，在超大规模实例上实现500倍提速。
A Quadratically Convergent Sequential Programming Method for Second-Order Cone Programs Capable of Warm Starts
针对线性二阶锥规划，提出基于序列二次规划框架的新方法，利用多面体外逼近克服不可微性，支持热启动并实现局部二次收敛，精度优于内点法。
Transformer-Based Warm-Starting for Feasible and Optimal Terminal Approach to Tumbling Objects with Space Manipulators
针对空间机械臂末端接近翻滚目标的实时轨迹生成问题，提出基于因果Transformer的热启动方法，通过分解规划并热启动姿态-力矩分配阶段，在300个测试场景中减少28%迭代次数和23%运行时间，同时保持控制成本分布。
Learning Warm Starts for the Simplex Method from Measured Solver Cost
该研究提出CostStart方法，结合监督基预测与基于CPU指令数的策略选择，在25类线性规划上较默认启动减半求解时间，且比两种已发表方法快1.4-2.2倍。
Bilevel Optimization with a Lower-level Contraction: Optimal Sample Complexity without Warm-start
本文针对无热启动的双层优化问题，提出下层随机不动点迭代与上层投影非精确梯度下降的简单方法，在随机和确定性设置下分别实现$O(ε^{-2})$和$\ ilde{O}(ε^{-1})$的阶数最优样本复杂度，并简化了分析。
Physics-Informed Bayesian Optimization Warm-Starts for Sequential Convex Programming in Asteroid Surface Hopping
该研究针对小行星433爱神星表面跳跃的燃料最优问题，提出物理信息贝叶斯优化热启动方法，结合序列凸规划实现高精度、低燃料消耗的轨迹规划，减少迭代次数并消除收敛失败。
Bridging Classical and Quantum with SDP initialized warm-starts for QAOA
针对含噪声量子设备仅能运行低深度QAOA的局限，提出用Max-Cut问题的低秩SDP松弛解做经典预处理的热启动QAOA-Warm，低深度下性能更优、训练更快，并提供实验与理论支撑。
A Block Lanczos with Warm Start Technique for Accelerating Nuclear Norm Minimization Algorithms
提出块Lanczos热启动（BLWS）技术，利用前次迭代的主奇异子空间初始化块Lanczos过程以加速核范数最小化算法中的部分SVD计算，实验表明可加速2-3倍。
Learning-Augmented Scalable Linear Assignment Problem Optimization via Neural Dual Warm-Starts
提出一种学习增强框架，通过预测对偶变量热启动精确求解器，并设计轻量级行独立架构RowDualNet避免O(N^2)内存瓶颈，实现可扩展的神经热启动，在保持最优性的同时获得超过2倍加速。
Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine
提出去混杂暖启动汤普森采样（DWTS），利用双重去偏LASSO利用混杂观测数据初始化LinTS先验，在合成和真实心血管数据上降低累积遗憾，提升临床试验效率并支持个性化治疗。
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