{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T19:03:45Z","timestamp":1782587025352,"version":"3.54.5"},"reference-count":83,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,4,13]],"date-time":"2012-04-13T00:00:00Z","timestamp":1334275200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s10957-012-0039-0","type":"journal-article","created":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T16:50:04Z","timestamp":1334249404000},"page":"382-417","source":"Crossref","is-referenced-by-count":90,"title":["A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory"],"prefix":"10.1007","volume":"154","author":[{"given":"Gregory","family":"Lantoine","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan P.","family":"Russell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2012,4,13]]},"reference":[{"key":"39_CR1","series-title":"International Series of Numerical Mathematics","first-page":"207","volume-title":"SQP Methods and Their Application to Numerical Optimal Control","author":"A. Barclay","year":"1998","unstructured":"Barclay, A., Gil, P.E., Rosen, J.B.: In: SQP Methods and Their Application to Numerical Optimal Control. International Series of Numerical Mathematics, vol. 124, pp. 207\u2013222 (1998)"},{"key":"39_CR2","volume-title":"A Method for Nonlinear Constraints in Minimization Problems","author":"M.J.D. Powell","year":"1969","unstructured":"Powell, M.J.D.: A Method for Nonlinear Constraints in Minimization Problems. Academic Press, London and New York (1969). R. Fletcher (ed.), optimization edition"},{"key":"39_CR3","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"M.R. Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12211-2","volume-title":"Lancelot: A Fortran Package for Large-Scale Nonlinear Optimization (Release A)","author":"A.R. Conn","year":"1992","unstructured":"Conn, A.R., Gould, G.I.M., Toint, P.L.: Lancelot: A Fortran Package for Large-Scale Nonlinear Optimization (Release A). Springer, Berlin (1992)"},{"key":"39_CR5","series-title":"Mathematical Programming Studies","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BFb0120949","volume-title":"Algorithms for Constrained Minimization of Smooth Nonlinear Functions","author":"B.A. Murtagh","year":"1982","unstructured":"Murtagh, B.A., Saunders, M.A.: A projected Lagrangian algorithm and its implementation for sparse non-linear constraints. In: Algorithms for Constrained Minimization of Smooth Nonlinear Functions. Mathematical Programming Studies, vol. 16, pp. 84\u2013117 (1982)"},{"key":"39_CR6","unstructured":"Wilson, R.B.: A simplicial method for convex programming. PhD thesis. Harvard University (1963)"},{"issue":"3","key":"39_CR7","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00932858","volume":"22","author":"S.P. Han","year":"1977","unstructured":"Han, S.P.: A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 22(3), 297\u2013309 (1977)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR8","volume-title":"Nonlinear Programming","author":"M.J.D. Powell","year":"1978","unstructured":"Powell, M.J.D.: The convergence of variable metric methods for nonlinearly constrained optimization calculations. In: Nonlinear Programming, vol.\u00a03. Academic Press, San Diego (1978)"},{"issue":"4","key":"39_CR9","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1137\/S1052623499350013","volume":"12","author":"P.E. Gill","year":"2002","unstructured":"Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP Algorithm for Large-Scale Constrained Optimization. SIAM J. Optim. 12(4), 979\u20131006 (2002)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"39_CR10","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/BF02192216","volume":"82","author":"J.T. Betts","year":"1994","unstructured":"Betts, J.T., Frank, P.D.: A sparse nonlinear optimization algorithm. J. Optim. Theory Appl. 82(3), 519\u2013541 (1994)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"39_CR11","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A. Wachter","year":"2006","unstructured":"Wachter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, mathematical programming. Math. Program. 106(1), 25\u201357 (2006)","journal-title":"Math. Program."},{"key":"39_CR12","volume-title":"4th International Conference on Astrodynamics Tools and Techniques","author":"T. Nikolayzik","year":"2010","unstructured":"Nikolayzik, T., Buskens, C.: WORHP (We Optimize Really Huge Problems). In: 4th International Conference on Astrodynamics Tools and Techniques, Madrid, Spain, May (2010)"},{"key":"39_CR13","doi-asserted-by":"crossref","unstructured":"Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H.: User\u2019s guide for SOL\/NPSOL: a Fortran package for nonlinear programming. Report sol 83-12. Department of Operations Research, Stanford University, California (1983)","DOI":"10.2172\/5633733"},{"key":"39_CR14","unstructured":"Kraft, D.: A software package for sequential quadratic programming. Technical report DFVLR-FB 88-28, Institut f\u00fcr Dynamik der Flugsysteme, Koln, Germany (July 1988)"},{"key":"39_CR15","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1080\/10556789908805759","volume":"12","author":"R.J. Vanderbei","year":"1999","unstructured":"Vanderbei, R.J.: LOQO: an interior point code for quadratic programming. Optim. Methods Softw. 12, 451\u2013484 (1999)","journal-title":"Optim. Methods Softw."},{"key":"39_CR16","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/0-387-30065-1_4","volume-title":"Large Scale Nonlinear Optimization","author":"R.H. Byrd","year":"2006","unstructured":"Byrd, R.H., Nocedal, J., Waltz, R.A.: KNITRO: an integrated package for nonlinear optimization. In: Large Scale Nonlinear Optimization, pp. 35\u201359. Springer, Berlin (2006)"},{"key":"39_CR17","series-title":"Lecture Notes in Control and Information Sciences","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/BFb0006176","volume-title":"System Modeling and Optimization","author":"M.J.D. Powell","year":"1982","unstructured":"Powell, M.J.D.: Extensions to subroutine VF02. In: Drenick, R.F., Kozin, F. (eds.) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol. 38, pp. 529\u2013538. Springer, Berlin (1982)"},{"key":"39_CR18","unstructured":"Harwell subroutine library. http:\/\/www.hsl.rl.ac.uk\/"},{"issue":"3","key":"39_CR19","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1145\/192115.192124","volume":"20","author":"D. Kraft","year":"1994","unstructured":"Kraft, D.: Algorithm 733: Tomp\u2013Fortran modules for optimal control calculations. ACM Trans. Math. Softw. 20(3), 262\u2013281 (1994)","journal-title":"ACM Trans. Math. Softw."},{"key":"39_CR20","unstructured":"Ross, I.M.: User\u2019s manual for DIDO (ver. pr. 13): a Matlab application package for solving optimal control problems. Technical report 04-01.0, Naval Postgraduate School, Monterey, CA, February (2004)"},{"issue":"2","key":"39_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1731022.1731032","volume":"37","author":"A.V. Rao","year":"2010","unstructured":"Rao, A.V., Benson, D.A., Darby, C., Patterson, M.A., Francolin, C., Sanders, I., Huntington, G.T.: Algorithm 902: GPOPS, a Matlab software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans. Math. Softw. 37(2), 1\u201339 (2010)","journal-title":"ACM Trans. Math. Softw."},{"key":"39_CR22","volume-title":"AAS\/AIAA Astrodynamics Specialist Conference and Exhibit","author":"J.A. Sims","year":"2006","unstructured":"Sims, J.A., Finlayson, P., Rinderle, E., Vavrina, M., Kowalkowski, T.: Implementation of a low-thrust trajectory optimization algorithm for preliminary design. In: AAS\/AIAA Astrodynamics Specialist Conference and Exhibit, Keystone, CO, August (2006). No. AIAA-2006-674"},{"key":"39_CR23","unstructured":"Franke, R.: Omuses tool for the optimization of multistage systems and HQP a solver for sparse nonlinear optimization, version 1.5. Technical report, Technical University of Ilmenau (1998)"},{"issue":"1","key":"39_CR24","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S0377-0427(00)00310-1","volume":"120","author":"P.E. Gill","year":"2000","unstructured":"Gill, P.E., Jay, L.O., Leonard, M.W., Petzold, L.R., Sharma, V.: An SQP method for the optimal control of large-scale dynamical systems. J. Comput. Appl. Math. 120(1), 197\u2013213 (2000)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"39_CR25","doi-asserted-by":"crossref","first-page":"515","DOI":"10.2478\/v10006-007-0043-y","volume":"17","author":"J. Blaszczyk","year":"2007","unstructured":"Blaszczyk, J., Karbowski, A., Malinowski, K.: Object library of algorithms for dynamic optimization problems: benchmarking SQP and nonlinear interior point methods. Int. J. Appl. Math. Comput. Sci. 17(4), 515\u2013537 (2007)","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"39_CR26","unstructured":"Lantoine, G.: A methodology for robust optimization of Low-Thrust trajectories in multibody environments. PhD thesis. School of Aerospace Engineering, Georgia Institute of Technology, Georgia (2010)"},{"key":"39_CR27","unstructured":"Bullock, T.E.: Computation of optimal controls by a method based on second variations. PhD thesis. Department of Aeronautics and Astronautics, Stanford University, Palo Alto, CA (1966)"},{"key":"39_CR28","unstructured":"Wachter, A.: An interior point algorithm for Large-Scale nonlinear optimization with applications in process engineering. PhD thesis. Carnegie Mellon University, Pittsburgh, Pennsylvania (January 2002)"},{"key":"39_CR29","unstructured":"Liao, L.Z.: Optimal control approach for large scale unconstrained optimization problems (1995). http:\/\/www.citeseer.ist.psu.edu\/liao95optimal.html"},{"key":"39_CR30","volume-title":"Dynamic Programming","author":"R.E. Bellman","year":"1957","unstructured":"Bellman, R.E.: Dynamic Programming. Princeton University Press, Princeton (1957)"},{"issue":"1","key":"39_CR31","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0096-3003(84)90051-1","volume":"15","author":"S.J. Yakowitz","year":"1984","unstructured":"Yakowitz, S.J., Rutherford, B.: Computational aspects of discrete-time optimal control. Appl. Math. Comput. 15(1), 29\u201345 (1984)","journal-title":"Appl. Math. Comput."},{"key":"39_CR32","unstructured":"Liao, L.Z., Shoemaker, C.A.: Advantages of differential dynamic programming over newton\u2019s method for discrete-time optimal control problems. Technical report. Cornell University (1993)"},{"key":"39_CR33","volume-title":"Dynamic Programming and the Calculus of Variations","author":"S.E. Dreyfus","year":"1965","unstructured":"Dreyfus, S.E.: Dynamic Programming and the Calculus of Variations. Academic Press, New York (1965)"},{"key":"39_CR34","volume-title":"Dynamic Optimization","author":"A.E. Bryson","year":"1999","unstructured":"Bryson, A.E.: Dynamic Optimization. Addison-Wesley, Menlo Park (1999)"},{"key":"39_CR35","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1080\/00207176608921369","volume":"3","author":"D.Q. Mayne","year":"1966","unstructured":"Mayne, D.Q.: A second-order gradient method for determining optimal control of non-linear discrete time systems. Int. J. Control 3, 85\u201395 (1966)","journal-title":"Int. J. Control"},{"key":"39_CR36","volume-title":"Differential Dynamic Programming","author":"D.H. Jacobson","year":"1970","unstructured":"Jacobson, D.H., Mayne, D.Q.: Differential Dynamic Programming. Elsevier, New York (1970)"},{"key":"39_CR37","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.2514\/3.5955","volume":"8","author":"S. Gershwin","year":"1970","unstructured":"Gershwin, S., Jacobson, D.H.: A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer. AIAA J. 8, 1616\u20131626 (1970)","journal-title":"AIAA J."},{"key":"39_CR38","volume-title":"The Computational Theory of Optimal Control","author":"P. Dyer","year":"1970","unstructured":"Dyer, P., McReynolds, S.: In: The Computational Theory of Optimal Control. Academic Press, New York (1970)"},{"key":"39_CR39","first-page":"75","volume-title":"Control and Dynamical Systems: Advances in Theory and Applications","author":"S.J. Yakowitz","year":"1989","unstructured":"Yakowitz, S.J.: Algorithms and computational techniques in differential dynamic programming. In: Control and Dynamical Systems: Advances in Theory and Applications, vol. 31, pp. 75\u201391. Academic Press, New York (1989)"},{"key":"39_CR40","unstructured":"Whiffen, G.J., Sims, J.: Application of a novel optimal control algorithm to low-thrust trajectory optimization. No. AAS 01-209, February (2001)"},{"key":"39_CR41","volume-title":"Computational Mathematical Programming","author":"D. Kraft","year":"1985","unstructured":"Kraft, D.: On converting optimal control problems into nonlinear programming problems. In: Computational Mathematical Programming. Springer, Berlin (1985)"},{"issue":"1","key":"39_CR42","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02071065","volume":"37","author":"O.V. Stryk","year":"1992","unstructured":"Stryk, O.V., Bulirsch, R.: Direct and indirect methods for trajectory optimization. Ann. Oper. Res. 37(1), 357\u2013373 (1992)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"39_CR43","doi-asserted-by":"crossref","first-page":"57","DOI":"10.2514\/2.4033","volume":"20","author":"D.G. Hull","year":"1997","unstructured":"Hull, D.G.: Conversion of optimal control problems into parameter optimization problems. J. Guid. Control Dyn. 20(1), 57\u201360 (1997)","journal-title":"J. Guid. Control Dyn."},{"key":"39_CR44","first-page":"21","volume-title":"IFIP Advances in Information and Communication Technology, System Modeling and Optimization","author":"L.T. Biegler","year":"2009","unstructured":"Biegler, L.T.: Efficient nonlinear programming algorithms for chemical process control and operations. In: IFIP Advances in Information and Communication Technology, System Modeling and Optimization, vol. 312, pp. 21\u201335. Springer, Boston (2009)"},{"issue":"6","key":"39_CR45","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1061\/(ASCE)0733-9496(1994)120:6(962)","volume":"120","author":"S.A. Taghavi","year":"1994","unstructured":"Taghavi, S.A., Howitt, R.E., Marino, M.A.: Optimal control of ground-water quality management: nonlinear programming approach. J. Water Resour. Plan. Manag. 120(6), 962\u2013982 (1994)","journal-title":"J. Water Resour. Plan. Manag."},{"issue":"1","key":"39_CR46","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0021-9290(98)00135-3","volume":"32","author":"T. Spagele","year":"1999","unstructured":"Spagele, T., Kistner, A., Gollhofer, A.: A multi-phase optimal control technique for the simulation of a human vertical jump. J. Biomech. 32(1), 87\u201391 (1999)","journal-title":"J. Biomech."},{"issue":"4","key":"39_CR47","doi-asserted-by":"crossref","first-page":"994","DOI":"10.2514\/3.20934","volume":"15","author":"P.J. Enright","year":"1992","unstructured":"Enright, P.J., Conway, B.A.: Discrete approximations to optimal trajectories using direct transcription and nonlinear programming. J. Guid. Control Dyn. 15(4), 994\u20131002 (1992)","journal-title":"J. Guid. Control Dyn."},{"issue":"2","key":"39_CR48","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1137\/S1111111102409080","volume":"2","author":"J.T. Betts","year":"2003","unstructured":"Betts, J.T., Erb, S.O.: Optimal low thrust trajectories to the moon. SIAM J. Appl. Dyn. Syst. 2(2), 144\u2013170 (2003)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"39_CR49","doi-asserted-by":"crossref","DOI":"10.1515\/9781400874651","volume-title":"Applied Dynamic Programming","author":"R.E. Bellman","year":"1962","unstructured":"Bellman, R.E., Dreyfus, S.E.: Applied Dynamic Programming. Princeton University Press, Princeton (1962)"},{"issue":"1","key":"39_CR50","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10569-009-9224-3","volume":"105","author":"C. Colombo","year":"2009","unstructured":"Colombo, C., Vasile, M., Radice, G.: Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming. Celest. Mech. Dyn. Astron. 105(1), 75\u2013112 (2009)","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"39_CR51","unstructured":"Whiffen, G.J.: Static\/dynamic control for optimizing a useful objective. No. Patent 6496741, December (2002)"},{"issue":"9","key":"39_CR52","doi-asserted-by":"crossref","first-page":"3277","DOI":"10.1029\/93WR00928","volume":"29","author":"G.J. Whiffen","year":"1993","unstructured":"Whiffen, G.J., Shoemaker, C.A.: Nonlinear weighted feedback control of groundwater remediation under uncertainty. Water Resour. Res. 29(9), 3277\u20133289 (1993)","journal-title":"Water Resour. Res."},{"key":"39_CR53","volume-title":"AAS\/AIAA Astrodynamics Specialist Conference and Exhibit","author":"A.E. Petropoulos","year":"2008","unstructured":"Petropoulos, A.E., Russell, R.P.: Low-thrust transfers using primer vector theory and a second-order penalty method. In: AAS\/AIAA Astrodynamics Specialist Conference and Exhibit, Honolulu, HI (2008). No. AIAA-2008-6955"},{"key":"39_CR54","volume-title":"SICE 2003 Annual Conference","author":"J. Morimioto","year":"2003","unstructured":"Morimioto, J., Zeglin, G., Atkeson, C.G.: Minimax differential dynamic programming: application to a biped walking robot. In: SICE 2003 Annual Conference Fukui University, Japan, August (2003)"},{"issue":"3","key":"39_CR55","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/59.65900","volume":"5","author":"S.C. Chang","year":"1990","unstructured":"Chang, S.C., Chen, C.H., Fong, I.K., Luh, P.B.: Hydroelectric generation scheduling with an effective differential dynamic programming algorithm. IEEE Trans. Power Syst. 5(3), 737\u2013743 (1990)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"39_CR56","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF00369913","volume":"9","author":"T.C. Lin","year":"1991","unstructured":"Lin, T.C., Arora, J.S.: Differential dynamic programming for constrained optimal control. Part 1. Theoretical development. Comput. Mech. 9(1), 27\u201340 (1991)","journal-title":"Comput. Mech."},{"issue":"2","key":"39_CR57","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF01968530","volume":"3","author":"D.J.W. Ruxton","year":"1993","unstructured":"Ruxton, D.J.W.: Differential dynamic programming applied to continuous optimal control problems with state variable inequality constraints. Dyn. Control 3(2), 175\u2013185 (1993)","journal-title":"Dyn. Control"},{"issue":"1","key":"39_CR58","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/TAC.1978.1101692","volume":"23","author":"K. Ohno","year":"1978","unstructured":"Ohno, K.: A new approach to differential dynamic programming for discrete time systems. IEEE Trans. Autom. Control 23(1), 37\u201347 (1978)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"39_CR59","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TAC.1986.1104123","volume":"31","author":"S.J. Yakowitz","year":"1986","unstructured":"Yakowitz, S.J.: The stagewise Kuhn\u2013Tucker condition and differential dynamic programming. IEEE Trans. Autom. Control 31(1), 25\u201330 (1986)","journal-title":"IEEE Trans. Autom. Control"},{"key":"39_CR60","unstructured":"Derbel, N.: Sur l\u2019utilisation de la programmation dynamique diff\u00e9rentielle pour la commande optimale de syst\u00e8mes complexes. PhD thesis. INSA, Toulouse, France (March 1989)"},{"key":"39_CR61","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1002\/oca.876","volume":"30","author":"P. Patel","year":"2009","unstructured":"Patel, P., Scheeres, D.J.: A second order optimization algorithm using quadric control updates for multistage optimal control problems. Optim. Control Appl. Methods 30, 525\u2013536 (2009)","journal-title":"Optim. Control Appl. Methods"},{"key":"39_CR62","series-title":"Mathematical Concepts and Methods in Science and Engineering","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-28020-0","volume-title":"Constrained Optimization and Image Space Analysis. Volume 1: Separation of Sets and Optimality Conditions","author":"F. Giannessi","year":"2005","unstructured":"Giannessi, F.: Constrained Optimization and Image Space Analysis. Volume 1: Separation of Sets and Optimality Conditions, 1st edn. Mathematical Concepts and Methods in Science and Engineering. Springer, Berlin (2005)","edition":"1"},{"key":"39_CR63","doi-asserted-by":"crossref","DOI":"10.1002\/9781118723203","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"2000","unstructured":"Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley, New York (2000)","edition":"2"},{"issue":"6","key":"39_CR64","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1109\/9.86943","volume":"36","author":"L.Z. Liao","year":"1991","unstructured":"Liao, L.Z., Shoemaker, C.A.: Convergence in unconstrained discrete-time differential dynamic programming. IEEE Trans. Autom. Control 36(6), 692\u2013706 (1991)","journal-title":"IEEE Trans. Autom. Control"},{"key":"39_CR65","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"A.R. Conn","year":"2000","unstructured":"Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. SIAM, Philadelphia (2000)"},{"issue":"1","key":"39_CR66","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF01299158","volume":"4","author":"T.F. Coleman","year":"1995","unstructured":"Coleman, T.F., Liao, A.: An efficient trust region method for unconstrained discrete-time optimal control problems. Comput. Optim. Appl. 4(1), 47\u201366 (1995)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"39_CR67","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1145\/355841.355844","volume":"5","author":"P.E. Gill","year":"1979","unstructured":"Gill, P.E., Murray, W., Picken, S.M., Wright, M.H.: The design and structure of a Fortran program library for optimization. ACM Trans. Math. Softw. 5(3), 259\u2013283 (1979)","journal-title":"ACM Trans. Math. Softw."},{"issue":"4","key":"39_CR68","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1109\/59.476071","volume":"10","author":"J. Tang","year":"1995","unstructured":"Tang, J., Luh, P.B.: Hydrothermal scheduling via extended differential dynamic programming and mixed coordination. IEEE Trans. Power Syst. 10(4), 2021\u20132028 (1995)","journal-title":"IEEE Trans. Power Syst."},{"key":"39_CR69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9904-1943-07818-4","volume":"49","author":"R. Courant","year":"1945","unstructured":"Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc. 49, 1\u201323 (1945)","journal-title":"Bull. Am. Math. Soc."},{"issue":"1","key":"39_CR70","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10589-005-1066-7","volume":"31","author":"E.G. Birgin","year":"2005","unstructured":"Birgin, E.G., Castillo, R.A., Martinez, J.M.: Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl. 31(1), 31\u201355 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR71","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"B.P. Bertsekas","year":"1982","unstructured":"Bertsekas, B.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, San Diego (1982)"},{"issue":"1","key":"39_CR72","doi-asserted-by":"crossref","first-page":"72","DOI":"10.4208\/jcm.2009.09-m2924","volume":"28","author":"L. Niu","year":"2010","unstructured":"Niu, L., Yuan, Y.: A new trust-region algorithm for nonlinear constrained optimization. J. Comput. Math. 28(1), 72\u201386 (2010)","journal-title":"J. Comput. Math."},{"issue":"3","key":"39_CR73","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1137\/0313030","volume":"13","author":"D.P. Bertsekas","year":"1975","unstructured":"Bertsekas, D.P.: Combined primal\u2013dual and penalty methods for constrained minimization. SIAM J. Control Optim. 13(3), 521\u2013544 (1975)","journal-title":"SIAM J. Control Optim."},{"issue":"6","key":"39_CR74","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1080\/10556780410001733513","volume":"20","author":"Z. Dostal","year":"2005","unstructured":"Dostal, Z.: Semi-monotonic inexact augmented Lagrangians for quadratic programming with equality constraints. Optim. Methods Softw. 20(6), 715\u2013727 (2005)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"39_CR75","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF03256560","volume":"56","author":"M. Majji","year":"2008","unstructured":"Majji, M., Junkins, J.L., Turner, J.D.: High order methods for estimation of dynamic systems. J. Astronaut. Sci. 56(3), 401\u2013440 (2008)","journal-title":"J. Astronaut. Sci."},{"issue":"6","key":"39_CR76","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.2514\/1.29106","volume":"30","author":"R.S. Park","year":"2007","unstructured":"Park, R.S., Scheeres, D.J.: Nonlinear semi-analytic methods for trajectory estimation. J. Guid. Control Dyn. 30(6), 1668\u20131676 (2007)","journal-title":"J. Guid. Control Dyn."},{"issue":"5","key":"39_CR77","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1029\/WR015i005p01017","volume":"15","author":"D.M. Murray","year":"1979","unstructured":"Murray, D.M., Yakowitz, S.J.: Constrained differential dynamic programming and its application to multireservoir control. Water Resour. Res. 15(5), 1017\u20131027 (1979)","journal-title":"Water Resour. Res."},{"key":"39_CR78","volume-title":"Practical Optimization","author":"P.E. Gill","year":"1982","unstructured":"Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, San Diego (1982)"},{"key":"39_CR79","first-page":"481","volume-title":"Proceedings of 2nd Berkeley Symposium","author":"H.W. Kuhn","year":"1951","unstructured":"Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of 2nd Berkeley Symposium, pp. 481\u2013492. University of California Press, Berkeley (1951)"},{"issue":"5","key":"39_CR80","doi-asserted-by":"crossref","first-page":"1750","DOI":"10.1137\/S036012995279031","volume":"36","author":"J.E. Dennis","year":"1998","unstructured":"Dennis, J.E., Heinkenschloss, M., Vicente, L.N.: Trust-region interior-point SQP algorithms for a class of nonlinear programming problems. SIAM J. Control Optim. 36(5), 1750\u20131794 (1998)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"39_CR81","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1115\/1.2826677","volume":"120","author":"J.F. Rodriguez","year":"1998","unstructured":"Rodriguez, J.F., Renaud, J.E., Watson, L.T.: Trust region augmented Lagrangian methods for sequential response surface approximation and optimization. J. Mech. Des. 120(1), 58\u201366 (1998)","journal-title":"J. Mech. Des."},{"issue":"4","key":"39_CR82","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1137\/S1052623498345075","volume":"9","author":"C.J. Lin","year":"1999","unstructured":"Lin, C.J., Mor\u00e9, J.J.: Newton\u2019s method for large bound-constrained optimization problems. SIAM J. Optim. 9(4), 1100\u20131127 (1999)","journal-title":"SIAM J. Optim."},{"key":"39_CR83","volume-title":"4th International Conference on Astrodynamics Tools and Techniques","author":"C. Ocampo","year":"2010","unstructured":"Ocampo, C., Senent, J.S., Williams, J.: Theoretical foundation of Copernicus: a unified system for trajectory design and optimization. In: 4th International Conference on Astrodynamics Tools and Techniques, Madrid, Spain, May (2010)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0039-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-012-0039-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0039-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T04:12:03Z","timestamp":1713845523000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-012-0039-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,13]]},"references-count":83,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["39"],"URL":"https:\/\/doi.org\/10.1007\/s10957-012-0039-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,13]]}}}