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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Bibliographic Details
Published in:Optimization methods & software Vol. 39; no. 5; pp. 1104 - 1142
Main Authors: Pfeiffer, Kai, Kheddar, Abderrahmane
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.09.2024
Taylor & Francis Ltd
Subjects:
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
Lexicographical optimization
Numerical optimization
Multi objective optimization
Sparse nullspace
Filter methods
Hierarchical non-linear least-squares programming
Discrete optimal control
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary: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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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2024.2307467