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
Hlavní autoři: Pfeiffer, Kai, Kheddar, Abderrahmane
Médium: Journal Article
Jazyk:angličtina
Vydáno: 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.
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
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  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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Snippet We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete...
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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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