论文标题
升力，分区和项目：在存在数值错误的情况下，主动设定QP方法的参数复杂性认证
Lift, Partition, and Project: Parametric Complexity Certification of Active-Set QP Methods in the Presence of Numerical Errors
论文作者
论文摘要
当实时使用模型预测控制（MPC）来控制线性系统时，需要在有限的时间范围内解决二次程序（QPS）。最近，已经提出了几种参数方法，以证明有效QP求解器求解这些QP所需的计算数量。这些认证方法，因此确定可以在有限的时间范围内解决优化问题。但是，这些方法的缺点是，它们不考虑在求解器内部可能发生的数值错误，最终可能会导致乐观的复杂性界限，例如，如果求解器以单个精度实现。在本文中，我们提出了一个通用框架，可以将其纳入这些认证方法中的任何一个，以说明这种数值错误。
When Model Predictive Control (MPC) is used in real-time to control linear systems, quadratic programs (QPs) need to be solved within a limited time frame. Recently, several parametric methods have been proposed that certify the number of computations active-set QP solvers require to solve these QPs. These certification methods, hence, ascertain that the optimization problem can be solved within the limited time frame. A shortcoming in these methods is, however, that they do not account for numerical errors that might occur internally in the solvers, which ultimately might lead to optimistic complexity bounds if, for example, the solvers are implemented in single precision. In this paper we propose a general framework that can be incorporated in any of these certification methods to account for such numerical errors.
