This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), whose computation cost depends linearly on the prediction horizon and quadratically on the state and input dimensions. CDAL is simple to implement and does not require constructing explicitly the matrices of the quadratic programming problem to solve. To favor convergence speed, CDAL employs a reverse cyclic rule for the CD method, the accelerated Nesterov's scheme for updating the dual variables, and a simple diagonal preconditioner. We show that CDAL competes with other state-of-the-art first-order methods, both in case of unstable linear time-invariant and prediction models linearized at runtime. All numerical results are obtained from a very compact, library-free, C implementation of the proposed CDAL solver.

中文翻译：

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一种用于模型预测控制的简单快速的坐标下降增广拉格朗日求解器

本文提出了一种新颖的坐标下降增强拉格朗日 (CDAL) 求解器，用于线性的、可能参数变化的模型预测控制问题。在每次迭代中，通过坐标下降 (CD) 解决增广拉格朗日 (AL) 子问题，其计算成本线性取决于预测范围，二次取决于状态和输入维度。CDAL 实现起来很简单，不需要明确构造二次规划问题的矩阵来解决。为了加快收敛速度​​，CDAL 对 CD 方法采用了反向循环规则、用于更新对偶变量的加速 Nesterov 方案和简单的对角预处理器。我们表明 CDAL 与其他最先进的一阶方法竞争，在不稳定的线性时不变和预测模型在运行时线性化的情况下。所有数值结果都是从所提议的 CDAL 求解器的非常紧凑、无库的 C 实现中获得的。