一种高性能多参数二次规划求解器
A High-Performant Multi-Parametric Quadratic Programming Solver
AI总结：
本文提出基于组合邻接性的多参数二次规划显式解算法，避免复杂几何运算并减少组合枚举，相比 MPT、POP 实现约两个数量级加速。
摘要：
我们提出了一种用于计算多参数二次规划显式解的组合方法，该方法可用于计算线性模型预测控制的显式控制律。与基于几何邻接性的经典方法不同，所提方法基于组合邻接性。在引入组合邻接性的概念后，我们证明显式解依据该邻接性构成一个连通图。随后，我们利用这种连通性提出了一种计算显式解的算法。该算法的纯组合性质带来了计算优势，因为它能够避免高要求的几何操作（例如计算多面体的面）。与经典组合方法相比，所提方法通过利用组合连通性，需要考虑的组合更少。我们表明，与 MPT 和 POP 等最先进的软件包相比，所提方法的一种实现可带来约两个数量级的加速。
英文摘要：
We propose a combinatorial method for computing explicit solutions to multi-parametric quadratic programs, which can be used to compute explicit control laws for linear model predictive control. In contrast to classical methods, which are based on geometrical adjacency, the proposed method is based on combinatorial adjacency. After introducing the notion of combinatorial adjacency, we show that the explicit solution forms a connected graph in terms of it. We then leverage this connectedness to propose an algorithm that computes the explicit solution. The purely combinatorial nature of the algorithm leads to computational advantages since it enables demanding geometrical operations (such as computing facets of polytopes) to be avoided. Compared with classical combinatorial methods, the proposed method requires fewer combinations to be considered by exploiting combinatorial connectedness. We show that an implementation of the proposed method can yield a speedup of about two orders of magnitude compared with state-of-the-art software packages such as MPT and POP.
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