PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS
In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalization error for a class of penalty terms, and we show that variations of Newton's method can be used to o...
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1826305277664690176 |
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| author | Witte, J Reisinger, C |
| author_facet | Witte, J Reisinger, C |
| author_sort | Witte, J |
| collection | OXFORD |
| description | In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalization error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalized equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods. © 2012 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-07T06:30:28Z |
| format | Journal article |
| id | oxford-uuid:f5cff4a5-1d9e-4f14-aef3-4de7f13e7a1a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:30:28Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:f5cff4a5-1d9e-4f14-aef3-4de7f13e7a1a2022-03-27T12:30:10ZPENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f5cff4a5-1d9e-4f14-aef3-4de7f13e7a1aEnglishSymplectic Elements at Oxford2012Witte, JReisinger, CIn this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalization error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalized equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods. © 2012 Society for Industrial and Applied Mathematics. |
| spellingShingle | Witte, J Reisinger, C PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title | PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title_full | PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title_fullStr | PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title_full_unstemmed | PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title_short | PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS |
| title_sort | penalty methods for the solution of discrete hjb equations continuous control and obstacle problems |
| work_keys_str_mv | AT wittej penaltymethodsforthesolutionofdiscretehjbequationscontinuouscontrolandobstacleproblems AT reisingerc penaltymethodsforthesolutionofdiscretehjbequationscontinuouscontrolandobstacleproblems |