zbMATH — the first resource for mathematics

Interactive dynamic optimization server – connecting one modelling language with many solvers. (English) Zbl 1301.49088
Summary: This paper presents a newly deployed server, Interactive Dynamic Optimization Server (IDOS), devoted to solving optimal control problems. Development and deployment of the Interactive Dynamic Optimization Server is a result of a project funded by NCBiR (National Center for Research and Development in Poland) under grant R02-0009-06 (henceforth called briefly the IDOS project). The aim of the project was to develop a prototype, online-accessible environment providing the service of solving dynamic optimization problems. One of the goals of the project was also to propose a modelling language (Dynamic Optimization Modelling Language, DOML) for defining optimal control problems - in a way that would not depend on constructs borrowed from concrete (lower level) programming languages. As a result, a user can specify his problem in a programming-language-neutral manner and use the server to attempt to solve it. The paper presents the workings of the server, the modelling language proposed (DOML) and an example of a problem specified in DOML and solved with IDOS.

49M37 Numerical methods based on nonlinear programming
93C15 Control/observation systems governed by ordinary differential equations
90C90 Applications of mathematical programming
68N20 Theory of compilers and interpreters
Full Text: DOI
[1] Abhishek K., FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs · Zbl 1243.90142
[2] Åkesson J., Modeling and Optimization with Optimica and JModelica.org – Languages and Tools for Solving Large-Scale Dynamic Optimization Problems (2009)
[3] DOI: 10.1007/978-3-0348-8497-6_11 · doi:10.1007/978-3-0348-8497-6_11
[4] DOI: 10.1007/BF02191662 · Zbl 0819.90091 · doi:10.1007/BF02191662
[5] Błaszczyk J., Int. J. Appl. Math. Comput. Sci. (Poland) 17 pp 515– (2007)
[6] DOI: 10.1016/j.disopt.2006.10.011 · Zbl 1151.90028 · doi:10.1016/j.disopt.2006.10.011
[7] DOI: 10.1007/s10107-008-0212-2 · Zbl 1163.90013 · doi:10.1007/s10107-008-0212-2
[8] Bonami P., BONMIN User’s Manual (2009)
[9] DOI: 10.1007/BF02592064 · Zbl 0619.90052 · doi:10.1007/BF02592064
[10] DOI: 10.1007/BF01581153 · Zbl 0833.90088 · doi:10.1007/BF01581153
[11] R. Franke,Anwendung von Interior-Point-Methoden zur Lösung zeitdiskreter Optimalsteuerungsprobleme, Master’s thesis, Techniche Universität Ilmenau, Fakultät für Informatik und Automatsierung, Institut für Automatisierungs- und Systemtechnik Fachgebiet Dynamik und Simulation ökologischer Systeme, Ilmenau, Germany, October 1994 (in German).
[12] R. Franke,OMUSES – A Tool for the Optimization of Multistage Systems and HQP – A Solver for Sparse Nonlinear Optimization. Version 1.5, Department of Automation and Systems Engineering, Technical University of Ilmenau, Ilmenau, Germany, September 1998.
[13] DOI: 10.1007/978-1-4612-1996-5_6 · doi:10.1007/978-1-4612-1996-5_6
[14] M. Gerdts, User’s Guide OC-ODE,Optimal Control of Ordinary-Differential Equations, Version 1.4, Institut für Mathematik, Universität Wüurzburg, Wüurzburg, 17 August 2010.
[15] Gobat J. I., Computer Science Technical Report CS94-376 (2005)
[16] J. Gondzio,Multiple centrality corrections in a primal-dual method for linear programming, Technical Report 1994.20, Department of Management Studies, University of Geneva, Geneva, Switzerland, November 1994. · Zbl 0860.90084
[17] DOI: 10.1145/229473.229474 · Zbl 0884.65015 · doi:10.1145/229473.229474
[18] Gropp W., Approximation Theory and Optimization pp 167– (1997)
[19] Hairer E., The Numerical Solution of Differential–Algebraic Equations by Runge–Kutta Methods (1989) · Zbl 0683.65050 · doi:10.1007/BFb0093947
[20] Hairer E., Solving Ordinary Differential Equations I (2008)
[21] DOI: 10.1007/978-3-642-05221-7 · Zbl 1192.65097 · doi:10.1007/978-3-642-05221-7
[22] F. Hecht, S. Auliac, O. Pironneau, J. Morice, A. Le Hyaric, and K. Ohtsuka, Freefem++ documentation on the web at http://www.freefem.org/ff++, Third Edition Version 3.22, Laboratoire J-L. Lions, Pierre et Marie Curie University, Paris, 2013.
[23] Martinon P., BOCOP v1.0.3 – User Guide, BOCOP – The optimal control solver (2012)
[24] JModelica.org Home Page, Modelon AB. Available at http://www.jmodelica.org/
[25] DOI: 10.1137/0802028 · Zbl 0773.90047 · doi:10.1137/0802028
[26] Modelica Association, Modelica – A Unified Object-Oriented Language For Systems Modeling. Language Specification v3.3 (2012)
[27] DOI: 10.1007/BF00939277 · Zbl 0577.49022 · doi:10.1007/BF00939277
[28] H.J. Oberle and W. Grimm,BNDSCO -A Program for the Numerical Solution of Optimal Control Problems, Report No. 515 der DFVLR, German Test and Research Institute for Aviation and Space Flight, 1989.
[29] DOI: 10.1137/0909014 · Zbl 0643.65039 · doi:10.1137/0909014
[30] DOI: 10.1007/BFb0067703 · doi:10.1007/BFb0067703
[31] Pytlak R., Numerical Procedures for Optimal Control Problems with State Constraints 1707 (1999) · Zbl 0928.49002 · doi:10.1007/BFb0097244
[32] Pytlak R., J. Discret. Dyn. Nat. Soc. (USA) 29 pp 1– (2011)
[33] DOI: 10.1016/0098-1354(92)80028-8 · doi:10.1016/0098-1354(92)80028-8
[34] DOI: 10.1023/A:1022690711754 · Zbl 0886.90140 · doi:10.1023/A:1022690711754
[35] de Souza P. N., The Maxima Book (2004)
[36] DOI: 10.1007/s10107-004-0559-y · Zbl 1134.90542 · doi:10.1007/s10107-004-0559-y
[37] DOI: 10.1007/BF00940784 · Zbl 0796.49034 · doi:10.1007/BF00940784
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.