We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter tailored to prioritized non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-squares programming via a globally convergent sequential quadratic programming step-filter. Leveraging a condition on the trust-region or the filter initialization, our hierarchical step-filter maintains this global convergence property. The hierarchical least-squares programming sub-problems are solved via a sparse nullspace method based interior point method. It is based on an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. It is also here that we propose a nullspace trust region adaptation method towards a comprehensive hierarchical step-filter. We demonstrate the computational efficiency of the hierarchical solver on typical test functions like the Rosenbrock and Himmelblau's functions, inverse kinematics problems and optimal control.
翻译:我们提出了一个按等级排列的最底层编程求解器,配有信任区和分级的分步过滤器,适合优先的非线性最佳控制。它基于一个等级级的分步过滤器,通过一个全球趋同的连续四级编程分步过滤器,解决非线级最低平方编程的每个优先级别。利用信任区或过滤器初始化的条件,我们的分步过滤器维持着这一全球趋同属性。以稀有的空空方法为基础的内点方法解决了等级最低层的分步编程问题。它基于有效使用回溯算法计算无线空空空空间基数的带宽度矩阵。我们在这里还提出了一个空空信任区适应方法,用于一个全面的分级分步过滤器。我们展示了等级解器对典型测试功能的计算效率,如罗森布罗克和喜梅尔布劳的功能、反运动问题和最佳控制。