Sequential hierarchical least-squares programming for prioritized non-linear optimal control
We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-sq...
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| Vydáno v: | Optimization methods & software Ročník 39; číslo 5; s. 1104 - 1142 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Abingdon
Taylor & Francis
02.09.2024
Taylor & Francis Ltd |
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| ISSN: | 1055-6788, 1029-4937 |
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| Abstract | We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete 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 reduced Hessian based interior point method. It leverages an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. We propose a nullspace trust region adaptation method embedded within the sub-problem solver 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 prioritized discrete non-linear optimal control. |
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| AbstractList | We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete 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 reduced Hessian based interior point method. It leverages an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. We propose a nullspace trust region adaptation method embedded within the sub-problem solver 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 prioritized discrete non-linear optimal control. |
| Author | Pfeiffer, Kai Kheddar, Abderrahmane |
| Author_xml | – sequence: 1 givenname: Kai surname: Pfeiffer fullname: Pfeiffer, Kai email: kaipfeifferrobotics@gmail.com organization: Nanyang Technological University – sequence: 2 givenname: Abderrahmane surname: Kheddar fullname: Kheddar, Abderrahmane organization: University of Montpellier |
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| Keywords | Lexicographical optimization Numerical optimization Multi objective optimization Sparse nullspace Filter methods Hierarchical non-linear least-squares programming Discrete optimal control |
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| SubjectTerms | Algorithms Bioinformatics Computer Science discrete optimal control filter methods hierarchical non-linear least-squares programming Inverse kinematics Least squares lexicographical optimization multi objective optimization Nonlinear control Numerical optimization Optimal control Quadratic programming Solvers sparse nullspace |
| Title | Sequential hierarchical least-squares programming for prioritized non-linear optimal control |
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