Graph-based algorithms for the efficient solution of optimization problems involving monotone functions
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, in the l...
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| Published in | Computational optimization and applications Vol. 73; no. 1; pp. 101 - 128 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.05.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0926-6003 1573-2894 |
| DOI | 10.1007/s10589-019-00070-4 |
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| Abstract | In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, in the linear case we show that the proposed algorithms outperform generic commercial solvers. |
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| AbstractList | In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, in the linear case we show that the proposed algorithms outperform generic commercial solvers. |
| Author | Consolini, Luca Locatelli, Marco Laurini, Mattia |
| Author_xml | – sequence: 1 givenname: Luca surname: Consolini fullname: Consolini, Luca organization: Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma – sequence: 2 givenname: Mattia surname: Laurini fullname: Laurini, Mattia organization: Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma – sequence: 3 givenname: Marco orcidid: 0000-0001-7138-8653 surname: Locatelli fullname: Locatelli, Marco email: marco.locatelli@unipr.it organization: Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma |
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| CitedBy_id | crossref_primary_10_1109_TAC_2021_3060706 crossref_primary_10_1080_23311916_2020_1782710 crossref_primary_10_1109_TASE_2021_3111758 |
| Cites_doi | 10.1007/s10589-017-9978-6 10.1007/978-0-387-21593-8 10.1093/imamci/17.2.167 10.1016/j.sysconle.2017.02.001 10.1016/S0375-9601(99)00757-4 10.1017/CBO9780511809088 10.1016/0020-0190(77)90002-3 10.1109/TSMCB.2012.2216523 10.1080/10556780903087124 10.1109/TSMCB.2008.926614 10.1126/science.286.5439.509 10.1109/CDC.2016.7799408 10.1109/MED.2016.7536010 |
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| Keywords | 06B23 65B99 Computational methods 90-04 90C35 Acceleration of convergence 90-08 90C39 Linear programming Dynamic programming Complete lattices |
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| References | Bardi, Capuzzo-Dolcetta (CR3) 2008 Consolini, Locatelli, Minari, Piazzi (CR8) 2017; 103 Wang, Gao, Teo (CR18) 2000; 17 CR6 CR7 Newman, Watts (CR17) 1999; 263 Davey, Priestley (CR9) 2002 CR15 CR12 CR11 Liu, Wei (CR16) 2013; 43 Holme, Kim (CR13) 2002; 65 Barabási, Albert (CR2) 1999; 286 Granas, Dugundji (CR10) 2003 Cabassi, Consolini, Locatelli (CR5) 2018; 70 Belotti, Lee, Liberti, Margot, Wächter (CR4) 2009; 24 Knuth (CR14) 1976; 6 Al-Tamimi, Lewis, Abu-Khalaf (CR1) 2008; 38 70_CR15 P Holme (70_CR13) 2002; 65 70_CR7 70_CR6 A Granas (70_CR10) 2003 P Belotti (70_CR4) 2009; 24 70_CR11 MEJ Newman (70_CR17) 1999; 263 DE Knuth (70_CR14) 1976; 6 M Bardi (70_CR3) 2008 B Davey (70_CR9) 2002 70_CR12 D Liu (70_CR16) 2013; 43 A-L Barabási (70_CR2) 1999; 286 F Cabassi (70_CR5) 2018; 70 A Al-Tamimi (70_CR1) 2008; 38 S Wang (70_CR18) 2000; 17 L Consolini (70_CR8) 2017; 103 |
| References_xml | – volume: 70 start-page: 61 issue: 1 year: 2018 end-page: 90 ident: CR5 article-title: Time-optimal velocity planning by a bound-tightening technique publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9978-6 – year: 2008 ident: CR3 publication-title: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations – year: 2003 ident: CR10 publication-title: Fixed Point Theory. Springer Monographs in Mathematics doi: 10.1007/978-0-387-21593-8 – ident: CR15 – ident: CR12 – volume: 17 start-page: 167 issue: 2 year: 2000 end-page: 178 ident: CR18 article-title: An upwind finite-difference method for the approximation of viscosity solutions to Hamilton–Jacobi–Bellman equations publication-title: IMA J. Math. Control Inf. doi: 10.1093/imamci/17.2.167 – ident: CR11 – volume: 103 start-page: 50 year: 2017 end-page: 57 ident: CR8 article-title: An optimal complexity algorithm for minimum-time velocity planning publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2017.02.001 – volume: 263 start-page: 341 issue: 4–6 year: 1999 end-page: 346 ident: CR17 article-title: Renormalization group analysis of the small-world network model publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(99)00757-4 – year: 2002 ident: CR9 publication-title: Introduction to Lattices and Order doi: 10.1017/CBO9780511809088 – volume: 6 start-page: 1 issue: 1 year: 1976 end-page: 5 ident: CR14 article-title: A generalization of Dijkstra’s algorithm publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(77)90002-3 – volume: 43 start-page: 779 issue: 2 year: 2013 end-page: 789 ident: CR16 article-title: Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems publication-title: IEEE Trans. Cybern. doi: 10.1109/TSMCB.2012.2216523 – ident: CR6 – ident: CR7 – volume: 24 start-page: 597 issue: 4–5 year: 2009 end-page: 634 ident: CR4 article-title: Branching and bounds tightening techniques for non-convex MINLP publication-title: Optim. Methods Softw. doi: 10.1080/10556780903087124 – volume: 38 start-page: 943 issue: 4 year: 2008 end-page: 949 ident: CR1 article-title: Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof publication-title: IEEE Trans. Syst. Man Cybern. Part B (Cybern.) doi: 10.1109/TSMCB.2008.926614 – volume: 65 start-page: 1 issue: 026107 year: 2002 end-page: 4 ident: CR13 article-title: Growing scale-free networks with tunable clustering publication-title: Phys. Rev. E – volume: 286 start-page: 509 year: 1999 end-page: 512 ident: CR2 article-title: Emergence of scaling in random networks publication-title: Science doi: 10.1126/science.286.5439.509 – volume: 286 start-page: 509 year: 1999 ident: 70_CR2 publication-title: Science doi: 10.1126/science.286.5439.509 – volume: 38 start-page: 943 issue: 4 year: 2008 ident: 70_CR1 publication-title: IEEE Trans. Syst. Man Cybern. Part B (Cybern.) doi: 10.1109/TSMCB.2008.926614 – volume-title: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations year: 2008 ident: 70_CR3 – volume: 24 start-page: 597 issue: 4–5 year: 2009 ident: 70_CR4 publication-title: Optim. Methods Softw. doi: 10.1080/10556780903087124 – ident: 70_CR11 – volume: 17 start-page: 167 issue: 2 year: 2000 ident: 70_CR18 publication-title: IMA J. Math. Control Inf. doi: 10.1093/imamci/17.2.167 – ident: 70_CR6 – volume: 70 start-page: 61 issue: 1 year: 2018 ident: 70_CR5 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9978-6 – volume-title: Fixed Point Theory. Springer Monographs in Mathematics year: 2003 ident: 70_CR10 doi: 10.1007/978-0-387-21593-8 – ident: 70_CR15 doi: 10.1109/CDC.2016.7799408 – volume: 6 start-page: 1 issue: 1 year: 1976 ident: 70_CR14 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(77)90002-3 – ident: 70_CR12 – volume-title: Introduction to Lattices and Order year: 2002 ident: 70_CR9 doi: 10.1017/CBO9780511809088 – volume: 43 start-page: 779 issue: 2 year: 2013 ident: 70_CR16 publication-title: IEEE Trans. Cybern. doi: 10.1109/TSMCB.2012.2216523 – volume: 263 start-page: 341 issue: 4–6 year: 1999 ident: 70_CR17 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(99)00757-4 – volume: 103 start-page: 50 year: 2017 ident: 70_CR8 publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2017.02.001 – volume: 65 start-page: 1 issue: 026107 year: 2002 ident: 70_CR13 publication-title: Phys. Rev. E – ident: 70_CR7 doi: 10.1109/MED.2016.7536010 |
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| SubjectTerms | Algorithms Convex and Discrete Geometry Dynamic programming Management Science Mathematics Mathematics and Statistics Monotone functions Operations Research Operations Research/Decision Theory Optimization Robot arms Solvers Statistics |
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| Title | Graph-based algorithms for the efficient solution of optimization problems involving monotone functions |
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