{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T14:59:53Z","timestamp":1758121193721,"version":"3.37.3"},"reference-count":78,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T00:00:00Z","timestamp":1712793600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T00:00:00Z","timestamp":1712793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100005251","name":"Office of Postsecondary Education","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005251","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10957-024-02431-4","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T12:01:56Z","timestamp":1712836916000},"page":"1116-1150","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Approaches for Constrained and Unconstrained, Static Optimization on the Special Euclidean Group SE(3)"],"prefix":"10.1007","volume":"201","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1722-5447","authenticated-orcid":false,"given":"Brennan","family":"McCann","sequence":"first","affiliation":[]},{"given":"Morad","family":"Nazari","sequence":"additional","affiliation":[]},{"given":"Christopher","family":"Petersen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"issue":"1","key":"2431_CR1","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1137\/100802529","volume":"22","author":"P-A Absil","year":"2012","unstructured":"Absil, P.-A., Malick, J\u00e9r\u00f4me.: Projection-like retractions on matrix manifolds. SIAM J. Optim. 22(1), 135\u2013158 (2012). https:\/\/doi.org\/10.1137\/100802529","journal-title":"SIAM J. Optim."},{"key":"2431_CR2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"P-A Absil","year":"2008","unstructured":"Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, New Jersey (2008)"},{"issue":"4","key":"2431_CR3","doi-asserted-by":"publisher","first-page":"1963","DOI":"10.1137\/16m1060248","volume":"9","author":"F Arrigoni","year":"2016","unstructured":"Arrigoni, F., Rossi, B., Fusiello, A.: Spectral synchronization of multiple views in SE(3). SIAM J. Imag. Sci. 9(4), 1963\u20131990 (2016). https:\/\/doi.org\/10.1137\/16m1060248","journal-title":"SIAM J. Imag. Sci."},{"issue":"5","key":"2431_CR4","doi-asserted-by":"publisher","first-page":"2919","DOI":"10.1137\/15m1038372","volume":"54","author":"V Ayala","year":"2016","unstructured":"Ayala, V., Jouan, P.: Almost-Riemannian geometry on lie groups. SIAM J. Control. Optim. 54(5), 2919\u20132947 (2016). https:\/\/doi.org\/10.1137\/15m1038372","journal-title":"SIAM J. Control. Optim."},{"doi-asserted-by":"publisher","unstructured":"Becigneul, G., Ganea, O.: Riemannian adaptive optimization methods. In: International Conference on Learning Representations. (2019). https:\/\/doi.org\/10.48550\/arXiv.1810.00760","key":"2431_CR5","DOI":"10.48550\/arXiv.1810.00760"},{"issue":"1","key":"2431_CR6","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1243\/0954406021524909","volume":"216","author":"C Belta","year":"2002","unstructured":"Belta, C., Kumar, V.: Euclidean metrics for motion generation on SE(3). Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 216(1), 47\u201360 (2002). https:\/\/doi.org\/10.1243\/0954406021524909","journal-title":"Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci."},{"issue":"2","key":"2431_CR7","doi-asserted-by":"publisher","first-page":"193","DOI":"10.2514\/2.4231","volume":"21","author":"JT Betts","year":"1998","unstructured":"Betts, J.T.: Survey of Numerical Methods for Trajectory Optimization. J. Guid. Control. Dyn. 21(2), 193\u2013207 (1998). https:\/\/doi.org\/10.2514\/2.4231","journal-title":"J. Guid. Control. Dyn."},{"doi-asserted-by":"publisher","unstructured":"Biggs, J., Holderbaum, W.: The geometry of optimal control solutions on some six dimensional lie groups. In: Proceedings of the 44th IEEE Conference on Decision and Control (2005). https:\/\/doi.org\/10.1109\/cdc.2005.1582359.","key":"2431_CR8","DOI":"10.1109\/cdc.2005.1582359."},{"doi-asserted-by":"publisher","unstructured":"Blanco, J.: A tutorial on transformation parameterizations and on-manifold optimization. (2010). https:\/\/doi.org\/10.48550\/arXiv.2103.15980","key":"2431_CR9","DOI":"10.48550\/arXiv.2103.15980"},{"key":"2431_CR10","volume-title":"An Introduction to Optimization on Smooth Manifolds","author":"N Boumal","year":"2020","unstructured":"Boumal, N.: An Introduction to Optimization on Smooth Manifolds. Princeton University Press, Princeton (2020)"},{"issue":"1","key":"2431_CR11","doi-asserted-by":"publisher","first-page":"2284","DOI":"10.3182\/20110828-6-it-1002.00542","volume":"44","author":"N Boumal","year":"2011","unstructured":"Boumal, N., Absil, P.-A.: A discrete regression method on manifolds and its application to data on SO(n). IFAC Proc. Vol. 44(1), 2284\u20132289 (2011). https:\/\/doi.org\/10.3182\/20110828-6-it-1002.00542","journal-title":"IFAC Proc. Vol."},{"issue":"42","key":"2431_CR12","first-page":"1455","volume":"15","author":"N Boumal","year":"2014","unstructured":"Boumal, N., Mishra, B., Absil, P.-A., Sepulchre, R. Manopt.: A MATLAB toolbox for optimization on manifolds. J. Mach. Learn. Res. 15(42), 1455\u20131459 (2014)","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"2431_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1137\/0107018","volume":"7","author":"JV Breakwell","year":"1959","unstructured":"Breakwell, J.V.: The optimization of trajectories. J. Soc. Ind. Appl. Math. 7(2), 215\u2013247 (1959). https:\/\/doi.org\/10.1137\/0107018","journal-title":"J. Soc. Ind. Appl. Math."},{"doi-asserted-by":"publisher","unstructured":"Brockett, R.W.: Differential geometry and the design of gradient algorithms. In: Differential Geometry: Partial Differential Equations on Manifolds (1993), pp. 69\u201392. https:\/\/doi.org\/10.1090\/pspum\/054.1\/1216576","key":"2431_CR14","DOI":"10.1090\/pspum\/054.1\/1216576"},{"key":"2431_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-7276-7","volume-title":"Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems","author":"F Bullo","year":"2005","unstructured":"Bullo, F., Lewis, A.D.: Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems. Springer (2005)"},{"doi-asserted-by":"publisher","unstructured":"Butcher, E.A., Maadani, M.: Consensus control of a multi-agent rigid body system on TSO(3)n and TSE(3)n. In: 2019 Sixth Indian Control Conference (ICC) (2019). https:\/\/doi.org\/10.1109\/icc47138.2019.9123241","key":"2431_CR16","DOI":"10.1109\/icc47138.2019.9123241"},{"issue":"9","key":"2431_CR17","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.2514\/1.g005039","volume":"43","author":"Q Dang","year":"2020","unstructured":"Dang, Q., Gui, H., Liu, K., Zhu, B.: Relaxed-constraint pinpoint lunar landing using geometric mechanics and model predictive control. J. Guid. Control. Dyn. 43(9), 1617\u20131630 (2020). https:\/\/doi.org\/10.2514\/1.g005039","journal-title":"J. Guid. Control. Dyn."},{"doi-asserted-by":"publisher","unstructured":"Dearing, T.L., Hauser, J., Petersen, C., Nicotra, M.M., Chen, X.: Attitude trajectory optimization and momentum conservation with control moment gyroscopes (2022). https:\/\/doi.org\/10.48550\/arXiv.2211.02110. arXiv:2211.02110 [math.OC]","key":"2431_CR18","DOI":"10.48550\/arXiv.2211.02110"},{"key":"2431_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2013\/292787","volume":"2013","author":"X Duan","year":"2013","unstructured":"Duan, X., Sun, H., Peng, L.: Riemannian means on special Euclidean group and Unipotent Matrices Group. Sci. World J. 2013, 1\u20139 (2013). https:\/\/doi.org\/10.1155\/2013\/292787","journal-title":"Sci. World J."},{"issue":"1","key":"2431_CR20","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1007\/s10957-022-02142-8","volume":"196","author":"N Eslami","year":"2022","unstructured":"Eslami, N., Najafi, B., Vaezpour, S.M.: A trust region method for solving multicriteria optimization problems on Riemannian manifolds. J. Optim. Theory Appl. 196(1), 212\u2013239 (2022). https:\/\/doi.org\/10.1007\/s10957-022-02142-8","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"2431_CR21","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1137\/18M1180633","volume":"29","author":"OP Ferreira","year":"2019","unstructured":"Ferreira, O.P., Louzeiro, M.S., Prudente, L.F.: Gradient method for optimization on Riemannian manifolds with lower bounded curvature. SIAM J. Optim. 29(4), 2517\u20132541 (2019). https:\/\/doi.org\/10.1137\/18M1180633","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2431_CR22","doi-asserted-by":"publisher","first-page":"1546","DOI":"10.1137\/20m1348522","volume":"31","author":"B Gao","year":"2021","unstructured":"Gao, B., Son, N.T., Absil, P.-A., Stykel, T.: Riemannian optimization on the symplectic Stiefel manifold. SIAM J. Optim. 31(2), 1546\u20131575 (2021). https:\/\/doi.org\/10.1137\/20m1348522","journal-title":"SIAM J. Optim."},{"key":"2431_CR23","volume-title":"Linear and Nonlinear Optimization","author":"I Griva","year":"2017","unstructured":"Griva, I., Nash, S.G., Sofer, A.: Linear and Nonlinear Optimization. Orient Blackswan Pvt Ltd, Bengaluru (2017)"},{"issue":"1","key":"2431_CR24","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.inffus.2011.08.003","volume":"14","author":"C Hertzberg","year":"2013","unstructured":"Hertzberg, C., Wagner, R., Frese, U., Schr\u00f6der, L.: Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds. Inf. Fusion 14(1), 57\u201377 (2013). https:\/\/doi.org\/10.1016\/j.inffus.2011.08.003","journal-title":"Inf. Fusion"},{"doi-asserted-by":"crossref","unstructured":"Holm, D.D.: Geometric Mechanics Part II: Rotating. Imperial College Press, Translating and Rolling (2011)","key":"2431_CR25","DOI":"10.1142\/p802"},{"doi-asserted-by":"publisher","unstructured":"Hou, M., Cho, S., Zhou, H., Edwards, C.R., Zhang, F.: Bounded cost path planning for underwater vehicles assisted by a time-invariant partitioned flow field model. In: Frontiers in Robotics and AI 8 (2021). https:\/\/doi.org\/10.3389\/frobt.2021.575267","key":"2431_CR26","DOI":"10.3389\/frobt.2021.575267"},{"doi-asserted-by":"publisher","unstructured":"Lai, Z., Yoshise, A. Riemannian Interior Point Methods for Constrained Optimization on Manifolds. (2022). https:\/\/doi.org\/10.48550\/arXiv.2203.09762. arXiv:2203.09762 [math.OC]","key":"2431_CR27","DOI":"10.48550\/arXiv.2203.09762"},{"doi-asserted-by":"publisher","unstructured":"Lee, T., Leok, M., McClamroch, N.H.: A combinatorial optimal control problem for spacecraft formation reconfiguration. In: 2007 46th IEEE Conference on Decision and Control. 2007, pp. 5370\u20135375. https:\/\/doi.org\/10.1109\/CDC.2007.4434143","key":"2431_CR28","DOI":"10.1109\/CDC.2007.4434143"},{"key":"2431_CR29","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s10883-008-9047-7","volume":"14","author":"T Lee","year":"2008","unstructured":"Lee, T., Leok, M., McClamroch, N.H.: Optimal attitude control of a rigid body using geometrically exact computations on. J. Dyn. Control Syst. 14, 465\u2013487 (2008). https:\/\/doi.org\/10.1007\/s10883-008-9047-7","journal-title":"J. Dyn. Control Syst."},{"doi-asserted-by":"publisher","unstructured":"Lee, T., McClamroch, N.H., Leok, M.: Optimal control of a rigid body using geometrically exact computations on SE(3). In: Proceedings of the 45th IEEE Conference on Decision and Control (2006). https:\/\/doi.org\/10.1109\/cdc.2006.376687","key":"2431_CR30","DOI":"10.1109\/cdc.2006.376687"},{"issue":"1896","key":"2431_CR31","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1098\/rspa.1992.0005","volume":"436","author":"M Lesser","year":"1992","unstructured":"Lesser, M.: A geometrical interpretation of Kane\u2019s equations. Proc. Math. Phys. Sci. 436(1896), 69\u201387 (1992). https:\/\/doi.org\/10.1098\/rspa.1992.0005","journal-title":"Proc. Math. Phys. Sci."},{"issue":"1","key":"2431_CR32","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0034-4877(96)87675-0","volume":"38","author":"AD Lewis","year":"1996","unstructured":"Lewis, A.D.: The geometry of the Gibbs-Appell equations and Gauss\u2019s principle of least constraint. Rep. Math. Phys. 38(1), 11\u201328 (1996). https:\/\/doi.org\/10.1016\/0034-4877(96)87675-0","journal-title":"Rep. Math. Phys."},{"key":"2431_CR33","doi-asserted-by":"publisher","DOI":"10.1002\/9781118122631","volume-title":"Optimal Control","author":"FL Lewis","year":"2012","unstructured":"Lewis, F.L., Syrmos, V.L., Vrabie, D.L.: Optimal Control. Wiley, New York (2012)"},{"doi-asserted-by":"publisher","unstructured":"Lezcano-Casado, M., Mart\u00ednez-Rubio, D.: Cheap orthogonal constraints in neural networks: a simple parametrization of the orthogonal and unitary group. arXiv:abs\/1901.08428 (2019). https:\/\/doi.org\/10.48550\/arXiv.1901.08428","key":"2431_CR34","DOI":"10.48550\/arXiv.1901.08428"},{"issue":"3","key":"2431_CR35","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1007\/s00245-019-09564-3","volume":"82","author":"C Liu","year":"2019","unstructured":"Liu, C., Boumal, N.: Simple algorithms for optimization on Riemannian manifolds with constraints. Appl. Math. Optim. 82(3), 949\u2013981 (2019). https:\/\/doi.org\/10.1007\/s00245-019-09564-3","journal-title":"Appl. Math. Optim."},{"issue":"1","key":"2431_CR36","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s42064-017-0003-8","volume":"1","author":"X Liu","year":"2017","unstructured":"Liu, X., Lu, P., Pan, B.: Survey of convex optimization for aerospace applications. Astrodynamics 1(1), 23\u201340 (2017). https:\/\/doi.org\/10.1007\/s42064-017-0003-8","journal-title":"Astrodynamics"},{"key":"2431_CR37","volume-title":"Optimization by Vector Space Methods","author":"DG Luenberger","year":"1969","unstructured":"Luenberger, D.G.: Optimization by Vector Space Methods. Wiley, New York (1969)"},{"issue":"1","key":"2431_CR38","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.ifacol.2016.03.040","volume":"49","author":"S Mathavaraj","year":"2016","unstructured":"Mathavaraj, S., Pandiyan, R., Padhi, R.: Optimal trajectory planning for multiphase lunar landing. IFAC-PapersOnLine 49(1), 124\u2013129 (2016). https:\/\/doi.org\/10.1016\/j.ifacol.2016.03.040","journal-title":"IFAC-PapersOnLine"},{"issue":"1","key":"2431_CR39","doi-asserted-by":"publisher","first-page":"29","DOI":"10.3934\/jgm.2022002","volume":"14","author":"B McCann","year":"2022","unstructured":"McCann, B., Nazari, M.: Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles. J. Geom. Mech. 14(1), 29\u201355 (2022). https:\/\/doi.org\/10.3934\/jgm.2022002","journal-title":"J. Geom. Mech."},{"unstructured":"McCann, B., Nazari, M.: Multibody dynamics on $${\\sf SE} (3)^{{n}}$$ with applications to optical system formation. In: AAS\/AIAA Astrodynamics Specialist Conference (2022)","key":"2431_CR40"},{"unstructured":"McCann, B., Nazari, M.: Optimal trajectory generation for rigid body landing dynamics on the special euclidean group. In: AAS\/AIAA Astrodynamics Specialist Conference AAS, pp. 23\u2013325 (2023)","key":"2431_CR41"},{"doi-asserted-by":"crossref","unstructured":"Michor, P.W.: Topics in Differential Geometry. American Mathematical Society (2008)","key":"2431_CR42","DOI":"10.1090\/gsm\/093"},{"key":"2431_CR43","doi-asserted-by":"publisher","DOI":"10.1515\/9781400881802","volume-title":"Morse Theory","author":"JW Milnor","year":"1963","unstructured":"Milnor, J.W.: Morse Theory. Princeton University Press, Princeton (1963)"},{"issue":"1","key":"2431_CR44","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1137\/140970860","volume":"26","author":"B Mishra","year":"2016","unstructured":"Mishra, B., Sepulchre, R.: Riemannian preconditioning. SIAM J. Optim. 26(1), 635\u2013660 (2016). https:\/\/doi.org\/10.1137\/140970860","journal-title":"SIAM J. Optim."},{"key":"2431_CR45","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.cam.2013.10.039","volume":"262","author":"A M\u00fcller","year":"2014","unstructured":"M\u00fcller, A., Terze, Z.: On the choice of configuration space for numerical Lie group integration of constrained rigid body systems. J. Comput. Appl. Math. 262, 3\u201313 (2014). https:\/\/doi.org\/10.1016\/j.cam.2013.10.039","journal-title":"J. Comput. Appl. Math."},{"key":"2431_CR46","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.mechmachtheory.2014.06.014","volume":"82","author":"A M\u00fcller","year":"2014","unstructured":"M\u00fcller, A., Terze, Z.: The significance of the configuration space Lie group for the constraint satisfaction in numerical time integration of multibody systems. Mech. Mach. Theory 82, 173\u2013202 (2014). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2014.06.014","journal-title":"Mech. Mach. Theory"},{"issue":"3","key":"2431_CR47","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1007\/10957-023-02224-1","volume":"197","author":"S Najafi","year":"2023","unstructured":"Najafi, S., Hajarian, M.: Multiobjective conjugate gradient methods on Riemannian manifolds. J. Optim. Theory Appl. 197(3), 1229\u20131248 (2023). https:\/\/doi.org\/10.1007\/10957-023-02224-1","journal-title":"J. Optim. Theory Appl."},{"doi-asserted-by":"publisher","unstructured":"Nazari, M., Maadani, M., Butcher, E.A., Yucelen, T.: Morse-Lyapunov-based control of rigid body motion on TSE(3) via backstepping. In: SciTech. (2018). https:\/\/doi.org\/10.2514\/6.2018-0602","key":"2431_CR48","DOI":"10.2514\/6.2018-0602"},{"key":"2431_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-023-02242-z","author":"D Nguyen","year":"2023","unstructured":"Nguyen, D.: Operator-valued formulas for Riemannian gradient and Hessian and families of tractable metrics in Riemannian optimization. J. Optim. Theory Appl. (2023). https:\/\/doi.org\/10.1007\/s10957-023-02242-z","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"2431_CR50","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1109\/LCSYS.2018.2874103","volume":"3","author":"A Nikhilraj","year":"2019","unstructured":"Nikhilraj, A., Simha, H., Priyadarshan, H.: Optimal energy trajectory generation for a quadrotor UAV using geometrically exact computations on SE(3). IEEE Control Syst. Lett. 3(1), 216\u2013221 (2019). https:\/\/doi.org\/10.1109\/LCSYS.2018.2874103","journal-title":"IEEE Control Syst. Lett."},{"issue":"2","key":"2431_CR51","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1137\/20m1370173","volume":"32","author":"M Obara","year":"2022","unstructured":"Obara, M., Okuno, T., Takeda, A.: Sequential quadratic optimization for nonlinear optimization problems on Riemannian manifolds. SIAM J. Optim. 32(2), 822\u2013853 (2022). https:\/\/doi.org\/10.1137\/20m1370173","journal-title":"SIAM J. Optim."},{"issue":"6","key":"2431_CR52","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1007\/s12555-011-0618-0","volume":"9","author":"B Park","year":"2011","unstructured":"Park, B., Tahk, M.: Three-dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site. Int. J. Control Autom. Syst. 9(6), 1164\u20131172 (2011). https:\/\/doi.org\/10.1007\/s12555-011-0618-0","journal-title":"Int. J. Control Autom. Syst."},{"issue":"1","key":"2431_CR53","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2558904","volume":"41","author":"IM Patterson","year":"2014","unstructured":"Patterson, I.M., Rao, A.V.: GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 41(1), 1\u201337 (2014). https:\/\/doi.org\/10.1145\/2558904","journal-title":"ACM Trans. Math. Softw."},{"issue":"2\u20133","key":"2431_CR54","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1177\/0278364918784361","volume":"38","author":"DM Rosen","year":"2019","unstructured":"Rosen, D.M., Carlone, L., Bandeira, A.S., Leonard, J.J.: SE-sync: a certifiably correct algorithm for synchronization over the special Euclidean group. Int. J. Robot. Res. 38(2\u20133), 95\u2013125 (2019). https:\/\/doi.org\/10.1177\/0278364918784361","journal-title":"Int. J. Robot. Res."},{"unstructured":"Ross, I.M., Fahroo, F.: User\u2019s manual for DIDO 2002: A MATLAB application package for dynamic optimization. In: Department of Aeronautics and Astronautics, NPS Technical Report AA-02-002, Naval Postgraduate School, Monterey, CA (2002)","key":"2431_CR55"},{"issue":"3","key":"2431_CR56","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s11370-022-00429-3","volume":"15","author":"AD Sabiha","year":"2022","unstructured":"Sabiha, A.D., Kamel, M.A., Said, E., Hussein, W.M.: Real-time path planning for autonomous vehicle based on teaching-learning-based optimization. Intel. Serv. Robot. 15(3), 381\u2013398 (2022). https:\/\/doi.org\/10.1007\/s11370-022-00429-3","journal-title":"Intel. Serv. Robot."},{"doi-asserted-by":"publisher","unstructured":"Sacchelli, L.: Short geodesics losing optimality in contact sub-Riemannian manifolds and stability of the 5-dimensional caustic. SIAM J. Control. Optim. 57(4), 2362\u20132391 (2019). https:\/\/doi.org\/10.1137\/18M1234710","key":"2431_CR57","DOI":"10.1137\/18M1234710"},{"doi-asserted-by":"publisher","unstructured":"Saccon, A., Hauser, J., Aguiar, A.P.: Optimal control on non-compact Lie groups: A projection operator approach. In: 49th IEEE Conference on Decision and Control (CDC) (2010). https:\/\/doi.org\/10.1109\/cdc.2010.5717195.","key":"2431_CR58","DOI":"10.1109\/cdc.2010.5717195."},{"key":"2431_CR59","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3108-8","volume-title":"Nonlinear Systems: Analysis, Stability, and Control","author":"S Sastry","year":"1999","unstructured":"Sastry, S.: Nonlinear Systems: Analysis, Stability, and Control. Springer, New York (1999)"},{"issue":"4","key":"2431_CR60","doi-asserted-by":"publisher","first-page":"2690","DOI":"10.1137\/21m1464178","volume":"32","author":"H Sato","year":"2022","unstructured":"Sato, H.: Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses. SIAM J. Optim. 32(4), 2690\u20132717 (2022). https:\/\/doi.org\/10.1137\/21m1464178","journal-title":"SIAM J. Optim."},{"doi-asserted-by":"crossref","unstructured":"Schaub, H., Junkins, J.L.: Analytical mechanics of space systems. American Institute of Aeronautics and Astronautics, Inc. (2018)","key":"2431_CR61","DOI":"10.2514\/4.105210"},{"doi-asserted-by":"publisher","unstructured":"Smith, S.: Optimization Techniques on Riemannian manifolds. In: Hamiltonian and Gradient Flows, Algorithms and Control (1995), pp. 113\u2013136. https:\/\/doi.org\/10.1090\/fic\/003\/09","key":"2431_CR62","DOI":"10.1090\/fic\/003\/09"},{"doi-asserted-by":"publisher","unstructured":"Soderlund, A., Phillips, S., Zaman, A., Petersen, C.D.: Autonomous satellite rendezvous and proximity operations via geometric control methods. In: AIAA Scitech 2021 Forum (2021). https:\/\/doi.org\/10.2514\/6.2021-0075","key":"2431_CR63","DOI":"10.2514\/6.2021-0075"},{"issue":"3","key":"2431_CR64","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/bf02741891","volume":"11","author":"K Spindler","year":"1998","unstructured":"Spindler, K.: Optimal control on Lie groups with applications to attitude control. Math. Control Signals Syst. 11(3), 197\u2013219 (1998). https:\/\/doi.org\/10.1007\/bf02741891","journal-title":"Math. Control Signals Syst."},{"key":"2431_CR65","first-page":"531","volume":"12","author":"K Spindler","year":"2013","unstructured":"Spindler, K.: Optimal control on lie groups: theory and applications. WSEAS Trans. Math. 12, 531\u2013542 (2013)","journal-title":"WSEAS Trans. Math."},{"issue":"1\u20134","key":"2431_CR66","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"J Sturm","year":"1999","unstructured":"Sturm, J.: Using SeDuMi 1.02, A MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11(1\u20134), 625\u2013653 (1999). https:\/\/doi.org\/10.1080\/10556789908805766","journal-title":"Optim. Methods Softw."},{"key":"2431_CR67","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.geomphys.2013.07.009","volume":"74","author":"A Suri","year":"2013","unstructured":"Suri, A.: Geometry of the double tangent bundles of Banach manifolds. J. Geom. Phys. 74, 91\u2013100 (2013). https:\/\/doi.org\/10.1016\/j.geomphys.2013.07.009","journal-title":"J. Geom. Phys."},{"doi-asserted-by":"publisher","unstructured":"Szmuk, M., Acikmese, B.: Successive Convexification for 6-DoF Mars Rocket Powered Landing with Free-Final-Time. In: 2018 AIAA Guidance, Navigation, and Control Conference (2018). https:\/\/doi.org\/10.2514\/6.2018-0617.","key":"2431_CR68","DOI":"10.2514\/6.2018-0617."},{"doi-asserted-by":"publisher","unstructured":"Szmuk, M., Reynolds, T., Acikmese, B., Mesbahi, M., Carson, J.M.: Successive convexification for 6-dof powered descent guidance with compound state-triggered constraints. In: AIAA Scitech 2019 Forum (2019). https:\/\/doi.org\/10.48550\/arXiv.1901.02181","key":"2431_CR69","DOI":"10.48550\/arXiv.1901.02181"},{"issue":"5","key":"2431_CR70","doi-asserted-by":"publisher","first-page":"3867","DOI":"10.1137\/15M1018022","volume":"56","author":"F Taringoo","year":"2018","unstructured":"Taringoo, F., et al.: Optimization methods on Riemannian manifolds via extremum seeking algorithms. SIAM J. Control. Optim. 56(5), 3867\u20133892 (2018). https:\/\/doi.org\/10.1137\/15M1018022","journal-title":"SIAM J. Control. Optim."},{"issue":"1","key":"2431_CR71","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2005","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2005). https:\/\/doi.org\/10.1007\/s10107-004-0559-y","journal-title":"Math. Program."},{"issue":"2","key":"2431_CR72","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s10589-021-00336-w","volume":"81","author":"Y Yamakawa","year":"2022","unstructured":"Yamakawa, Y., Sato, H.: Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method. Comput. Optim. Appl. 81(2), 397\u2013421 (2022). https:\/\/doi.org\/10.1007\/s10589-021-00336-w","journal-title":"Comput. Optim. Appl."},{"key":"2431_CR73","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.matcom.2020.09.019","volume":"181","author":"Z Yan","year":"2021","unstructured":"Yan, Z., Zhang, J., Tang, J.: Path planning for autonomous underwater vehicle based on an enhanced water wave optimization algorithm. Math. Comput. Simul. 181, 192\u2013241 (2021). https:\/\/doi.org\/10.1016\/j.matcom.2020.09.019","journal-title":"Math. Comput. Simul."},{"doi-asserted-by":"publisher","unstructured":"Zhang, H., Sra, S.: First-order methods for geodesically convex. Optimization (2016). https:\/\/doi.org\/10.48550\/ARXIV.1602.06053","key":"2431_CR74","DOI":"10.48550\/ARXIV.1602.06053"},{"key":"2431_CR75","first-page":"415","volume":"10","author":"L Zhang","year":"2013","unstructured":"Zhang, L., Yang, W., Song, R.: Optimality conditions for the nonlinear programming problems on Riemannian manifolds. Pac. J. Optim. 10, 415\u2013434 (2013)","journal-title":"Pac. J. Optim."},{"doi-asserted-by":"publisher","unstructured":"Zhang, Y., Sun, H., Jinyun Zhou, J., Pan, J., Hu, J., Jinghao Miao, J.: Optimal vehicle path planning using quadratic optimization for Baidu Apollo open platform. CoRR: abs\/2112.02132 (2021). https:\/\/doi.org\/10.48550\/arXiv.2112.02132.","key":"2431_CR76","DOI":"10.48550\/arXiv.2112.02132."},{"issue":"1","key":"2431_CR77","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10589-016-9883-4","volume":"67","author":"X Zhu","year":"2016","unstructured":"Zhu, X.: A Riemannian conjugate gradient method for optimization on the Stiefel manifold. Comput. Optim. Appl. 67(1), 73\u2013110 (2016). https:\/\/doi.org\/10.1007\/s10589-016-9883-4","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"2431_CR78","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1007\/s10589-020-00219-6","volume":"77","author":"X Zhu","year":"2020","unstructured":"Zhu, X., Sato, H.: Riemannian conjugate gradient methods with inverse retraction. Comput. Optim. Appl. 77(3), 779\u2013810 (2020). https:\/\/doi.org\/10.1007\/s10589-020-00219-6","journal-title":"Comput. Optim. Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02431-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-024-02431-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02431-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T07:17:47Z","timestamp":1719213467000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-024-02431-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,11]]},"references-count":78,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2431"],"URL":"https:\/\/doi.org\/10.1007\/s10957-024-02431-4","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2024,4,11]]},"assertion":[{"value":"10 June 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}