Inexact restoration and adaptive mesh refinement for optimal control
| dc.contributor.author | Banihashemi, N. | |
| dc.contributor.author | Kaya, C.Y. | |
| dc.date.issued | 2014 | |
| dc.description.abstract | A new adaptive mesh refinement algorithm is proposed for solving Euler discretization of state- and control-constrained optimal control problems. Our approach is designed to reduce the computational effort by applying the inexact restoration (IR) method, a numerical method for nonlinear programming problems, in an innovative way. The initial iterations of our algorithm start with a coarse mesh, which typically involves far fewer discretization points than the fine mesh over which we aim to obtain a solution. The coarse mesh is then refined adaptively, by using the sufficient conditions of convergence of the IR method. The resulting adaptive mesh refinement algorithm is convergent to a fine mesh solution, by virtue of convergence of the IR method. We illustrate the algorithm on a computationally challenging constrained optimal control problem involving a container crane. Numerical experiments demonstrate that significant computational savings can be achieved by the new adaptive mesh refinement algorithm over the fixed-mesh algorithm. Conceivably owing to the small number of variables at start, the adaptive mesh refinement algorithm appears to be more robust as well, i.e., it can find solutions with a much wider range of initial guesses, compared to the fixed-mesh algorithm. | |
| dc.identifier.citation | Journal of Industrial and Management Optimization, 2014; 10(2):521-542 | |
| dc.identifier.doi | 10.3934/jimo.2014.10.521 | |
| dc.identifier.issn | 1547-5816 | |
| dc.identifier.issn | 1553-166X | |
| dc.identifier.uri | https://hdl.handle.net/1959.8/153869 | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.rights | Copyright 2014 American Institute of Mathematical Sciences | |
| dc.source.uri | https://doi.org/10.3934/jimo.2014.10.521 | |
| dc.subject | adaptive mesh refinement | |
| dc.subject | container crane | |
| dc.subject | Euler discretization | |
| dc.subject | inexact restoration | |
| dc.subject | state and control-constrained optimal control | |
| dc.title | Inexact restoration and adaptive mesh refinement for optimal control | |
| dc.type | Journal article | |
| pubs.publication-status | Published | |
| ror.mmsid | 9915910039301831 |