论文标题
在参数约束最小二乘问题中减少变量数量
Reduction of the Number of Variables in Parametric Constrained Least-Squares Problems
论文作者
论文摘要
对于依赖参数向量的线性约束最小二乘问题，本文提出了减少涉及优化变量数量的技术。在通过QR分解以数值鲁棒的方式消除平等约束之后，我们提出了一种基于单数值分解（SVD）和无监督学习的技术，我们称为$ K $ -SVD，神经分类器和神经分类器自动将$ k $ nonlinear extorme的参数矢量自动划分为$ k $ nonlinear extime的设置，该变异使用原始问题较小的设置。对于由模型预测控制（MPC）制剂引起的参数约束最小二乘问题的特殊情况，我们提出了一种新颖且非常有效的QR分解方法，以消除平等性约束。该方法与SVD或$ K $ -SVD一起，提供了标准冷凝和移动阻塞的数字稳定性替代方案，并根据基于基础函数为MPC提供了其他复杂性降低方法。我们在数值测试和非线性基准过程的线性化MPC问题中显示了提出的技术的良好性能。
For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically robust way by QR factorization, we propose a technique based on singular value decomposition (SVD) and unsupervised learning, that we call $K$-SVD, and neural classifiers to automatically partition the set of parameter vectors in $K$ nonlinear regions in which the original problem is approximated by using a smaller set of variables. For the special case of parametric constrained least-squares problems that arise from model predictive control (MPC) formulations, we propose a novel and very efficient QR factorization method for equality constraint elimination. Together with SVD or $K$-SVD, the method provides a numerically robust alternative to standard condensing and move blocking, and to other complexity reduction methods for MPC based on basis functions. We show the good performance of the proposed techniques in numerical tests and in a linearized MPC problem of a nonlinear benchmark process.
