A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds | Paper Citation Record

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This paper cites IEEE Transactions on I nformation Theory 62(3), 1458–1484 (2015) https://doi.org/10.1109/TIT.2015.2457942.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds IEEE Transactions on I nformation Theory 62(3), 1458–1484 (2015) https://doi.org/10.1109/TIT.2015.2457942

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This paper cites IEEE Transactions on Robotics 34(5), 1252–1265 (2018) https://doi.org/10.1109/TRO.2018.2830390.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds IEEE Transactions on Robotics 34(5), 1252–1265 (2018) https://doi.org/10.1109/TRO.2018.2830390

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This paper cites Riemannian Direct Trajectory Optimization of Rigid Bodies on Matrix Lie Groups.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Riemannian Direct Trajectory Optimization of Rigid Bodies on Matrix Lie Groups

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This paper cites In: 2017 International Conference on Samplin g The- ory and Applications (SampTA), pp.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds In: 2017 International Conference on Samplin g The- ory and Applications (SampTA), pp

Reference 4

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This paper cites Advances in Neural Information Processing Systems 36 (2024) https://doi.org/10.52202/075280-3504.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Advances in Neural Information Processing Systems 36 (2024) https://doi.org/10.52202/075280-3504

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This paper cites Athena Scient iﬁc, Belmont, MA (2016).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Athena Scient iﬁc, Belmont, MA (2016)

Reference 6

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This paper cites In : Mixed Inte- ger Nonlinear Programming vol.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds In : Mixed Inte- ger Nonlinear Programming vol

Reference 7

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This paper cites SIAM Journal on Optimization 11(4), 1092– 1118 (2001) https://doi.org/10.1137/S1052623498344562.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 11(4), 1092– 1118 (2001) https://doi.org/10.1137/S1052623498344562

Reference 8

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This paper cites Optimization 71(6), 1603–1635 (2022) https://doi.org/10.1080/02331934.2020.1827406.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Optimization 71(6), 1603–1635 (2022) https://doi.org/10.1080/02331934.2020.1827406

Reference 9

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This paper cites Journal of Scientiﬁc Computing 102(2), 33 (2025) https://doi.org/10.1007/s10915-024-02743-7.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Scientiﬁc Computing 102(2), 33 (2025) https://doi.org/10.1007/s10915-024-02743-7

Reference 10

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This paper cites SIAM Journal on Control and Optimization 26(4), 788–811 (1988) https://doi.org/10.1137/0326046.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Control and Optimization 26(4), 788–811 (1988) https://doi.org/10.1137/0326046

Reference 11

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This paper cites Journal of Optimization Theory and Applications 95, 371–397 (1997) https://doi.org/10.1023/A:1022639306130.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization Theory and Applications 95, 371–397 (1997) https://doi.org/10.1023/A:1022639306130

Reference 12

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This paper cites Mathematical Programming 85(1), 81–106 (1999) https://doi.org/10.1007/s101070050047.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Mathematical Programming 85(1), 81–106 (1999) https://doi.org/10.1007/s101070050047

Reference 13

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This paper cites SIAM Jou rnal on Opti- mization 11(1), 113–132 (2000) https://doi.org/10.1137/S1052623499353935.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Jou rnal on Opti- mization 11(1), 113–132 (2000) https://doi.org/10.1137/S1052623499353935

Reference 14

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This paper cites SIAM Journal on Optimization 13(4), 1222– 1244 (2003) https://doi.org/10.1137/S1052623401383881.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 13(4), 1222– 1244 (2003) https://doi.org/10.1137/S1052623401383881

Reference 15

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This paper cites SIAM Journal on Optimization 17(2), 401–429 (2006) https://doi.org/10.1137/040605904.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 17(2), 401–429 (2006) https://doi.org/10.1137/040605904

Reference 16

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This paper cites Acta Mathematica Sinica, English Series 26(12), 2399–2420 (2010) https://doi.org/10.1007/s10114-010-7432-0.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Acta Mathematica Sinica, English Series 26(12), 2399–2420 (2010) https://doi.org/10.1007/s10114-010-7432-0

Reference 17

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This paper cites Journal of Optimization The ory and Applications 113(2), 297–323 (2002) https://doi.org/10.1023/A:1014882909302.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization The ory and Applications 113(2), 297–323 (2002) https://doi.org/10.1023/A:1014882909302

Reference 18

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This paper cites Journal of Optimization Theory and Applications 119(2), 281–316 (2003) https://doi.org/10.1023/B:JOTA.0000005447.36961.29.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization Theory and Applications 119(2), 281–316 (2003) https://doi.org/10.1023/B:JOTA.0000005447.36961.29

Reference 19

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This paper cites Optimization Methods & Software 29(6), 1238–1260 (2014) https://doi.org/10.1080/10556788.2013.879587.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Optimization Methods & Software 29(6), 1238–1260 (2014) https://doi.org/10.1080/10556788.2013.879587

Reference 20

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This paper cites Springer, New Y ork (2006).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Springer, New Y ork (2006)

Reference 21

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This paper cites Balkan Journal of Geometry and Its Applications 12(2) (2006).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Balkan Journal of Geometry and Its Applications 12(2) (2006)

Reference 22

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This paper cites Optimization 64(4), 1011–1031 (2015) https://doi.org/10.1080/02331934.2013.836650.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Optimization 64(4), 1011–1031 (2015) https://doi.org/10.1080/02331934.2013.836650

Reference 23

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This paper cites Computational Optimization and Applications 67(1), 73–110 (2017) https://doi.org/10.1007/s10589-016-9883-4.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Computational Optimization and Applications 67(1), 73–110 (2017) https://doi.org/10.1007/s10589-016-9883-4

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This paper cites Journal of Optimization Theory and Applications 190(1), 130–150 (2021) https://doi.org/10.1007/s10957-021-01874-3.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization Theory and Applications 190(1), 130–150 (2021) https://doi.org/10.1007/s10957-021-01874-3

Reference 25

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This paper cites Numerical Algorithms 94(1), 131–147 (2023) https://doi.org/10.1007/s11075-022-01495-5 34.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Numerical Algorithms 94(1), 131–147 (2023) https://doi.org/10.1007/s11075-022-01495-5 34

Reference 26

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This paper cites IMA Journal of Numerical Analysis 22(3), 359–390 (2002) https://doi.org/10.1093/imanum/22.3.359.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds IMA Journal of Numerical Analysis 22(3), 359–390 (2002) https://doi.org/10.1093/imanum/22.3.359

Reference 27

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 25(3), 1660–1685 (2015) https://doi.org/10.1137/140955483

Reference 28

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Numerical Algorithms 72(1), 57–90 (2016) https://doi.org/10.1007/s11075-015-0034-2

Reference 29

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This paper cites Foundations of Computational Mathematics 7(3), 303–330 (2007) https://doi.org/10.1007/s10208-005-0179-9.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Foundations of Computational Mathematics 7(3), 303–330 (2007) https://doi.org/10.1007/s10208-005-0179-9

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds IMA Journal of Numerical Analys is 36(3), 1167–1192 (2016) https://doi.org/10.1093/imanum/drv043

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This paper cites Princeton University Press, Princeton, NJ (2008).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Princeton University Press, Princeton, NJ (2008)

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This paper cites Cambridge University Press, Cambridge (2023).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Cambridge University Press, Cambridge (2023)

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Springer, Switzerland (2021)

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of the Operations Research Society of China 8, 199–248 (2020) https://doi.org/10.1007/s40305-020-00295-9

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Paciﬁc Journal of Optimiz ation 10(2), 415–434 (2014)

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This paper cites SIAM Journal on Optimization 29(4), 2423– 2444 (2019) https://doi.org/10.1137/18M1181602.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 29(4), 2423– 2444 (2019) https://doi.org/10.1137/18M1181602

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Applied Mathematics & Optimization 82(3), 949–981 (2020) https://doi.org/10.1007/s00245-019-09564-3

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This paper cites SIAM Journal on Optimization 31(3), 2255–2284 (2021) https://doi.org/10.1137/20M1341325.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 31(3), 2255–2284 (2021) https://doi.org/10.1137/20M1341325

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journa l on Optimization 32(2), 822–853 (2022) https://doi.org/10.1137/20M1370173

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization Theory and Applications 22(3), 297–309 (1977) https://doi.org/10.1007/BF00932858

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds PhD thesis, Imperial College London (Un iversity of London) (1978)

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This paper cites IEEE Transactions on Automatic Control 69(3), 2060–2066 (2024) https://doi.org/10.1109/TAC.2023.3318195.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds IEEE Transactions on Automatic Control 69(3), 2060–2066 (2024) https://doi.org/10.1109/TAC.2023.3318195

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This paper cites Journal of Optimization Theory and Application s, 1–37 (2024) https://doi.org/10.1007/s10957-024-02403-8.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Journal of Optimization Theory and Application s, 1–37 (2024) https://doi.org/10.1007/s10957-024-02403-8

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This paper cites Local near-quadratic convergence of Riemannian interior point methods.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Local near-quadratic convergence of Riemannian interior point methods

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This paper cites A primal-dual interior point trust region method for second-order stationary points of Riemannian inequality-constrained optimization problems.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds A primal-dual interior point trust region method for second-order stationary points of Riemannian inequality-constrained optimization problems

Reference 46

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This paper cites Mathematical Programming 11, 67–80 (1976) https://doi.org/10.1007/BF01580371.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Mathematical Programming 11, 67–80 (1976) https://doi.org/10.1007/BF01580371

Reference 47

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This paper cites SIAM Journal on Optimization 14(1), 173–199 (2003) https://doi.org/10.1137/S1052623401392123.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 14(1), 173–199 (2003) https://doi.org/10.1137/S1052623401392123

Reference 48

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This paper cites Optimiz ation 24(3-4), 269–284 (1992) https://doi.org/10.1080/02331939208843795.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Optimiz ation 24(3-4), 269–284 (1992) https://doi.org/10.1080/02331939208843795

Reference 49

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This paper cites In: Recent Advances in Nonsmooth Optimization, pp.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds In: Recent Advances in Nonsmooth Optimization, pp

Reference 50

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This paper cites Berlin-New York (1982).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Berlin-New York (1982)

Reference 51

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This paper cites SIA M Journal on Scientiﬁc and Statistical Somputing 4(3), 553–572 (1983) https://doi.org/10.1137/0904038.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIA M Journal on Scientiﬁc and Statistical Somputing 4(3), 553–572 (1983) https://doi.org/10.1137/0904038

Reference 52

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This paper cites Mathem atics of Opera- tions Research 5(1), 43–62 (1980) https://doi.org/10.1287/moor.5.1.43.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Mathem atics of Opera- tions Research 5(1), 43–62 (1980) https://doi.org/10.1287/moor.5.1.43

Reference 53

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This paper cites Mathema tical Program- ming 198(1), 855–897 (2023) https://doi.org/10.1007/s10107-022-01794-8.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Mathema tical Program- ming 198(1), 855–897 (2023) https://doi.org/10.1007/s10107-022-01794-8

Reference 54

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This paper cites The Journal of Machine Learning Rese arch 15(1), 1455–1459 (2014).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds The Journal of Machine Learning Rese arch 15(1), 1455–1459 (2014)

Reference 55

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This paper cites Advances in Computational Mathematics 46, 1–25 (2020) https://doi.org/10.1007/s10444-020-09779-x.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Advances in Computational Mathematics 46, 1–25 (2020) https://doi.org/10.1007/s10444-020-09779-x

Reference 56

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This paper cites SIAM Journal on Optimization 23(2), 1214–1236 (2013) https://doi.org/10.1137/110845768.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds SIAM Journal on Optimization 23(2), 1214–1236 (2013) https://doi.org/10.1137/110845768

Reference 57

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Numerische Mathemat ik 136(2), 523– 543 (2017) https://doi.org/10.1007/s00211-016-0848-4

Reference 58

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This paper cites European Journal of Operational Research 200(3), 645–657 (2010) https://doi.org/10.1016/j.ejor.2009.01.052.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds European Journal of Operational Research 200(3), 645–657 (2010) https://doi.org/10.1016/j.ejor.2009.01.052

Reference 59

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A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Unresolved cited work

Reference 60

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This paper cites Thus, the proof is complete.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Thus, the proof is complete

Reference 61

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This paper cites where the last inequality is due to ( 13).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds where the last inequality is due to ( 13)

Reference 62

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This paper cites (72) Similarly, for i /∈ I (x∗), we obtain { λk0 i zk } K′ → ˆλ∗ i = 0, i / ∈ I (x∗).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds (72) Similarly, for i /∈ I (x∗), we obtain { λk0 i zk } K′ → ˆλ∗ i = 0, i / ∈ I (x∗)

Reference 66

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This paper cites (73) Since ˆλ∗ E and ˆλ∗ I are not both zero, it follows from Assumption 4.1 that E(x∗) ⁄= E (i.e., x∗ ∈ F \FP ) and w > 0.

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds (73) Since ˆλ∗ E and ˆλ∗ I are not both zero, it follows from Assumption 4.1 that E(x∗) ⁄= E (i.e., x∗ ∈ F \FP ) and w > 0

Reference 67

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This paper cites For i /∈ E (x∗), we have β∗ i > 0, and thus { λk0 i zk } K′ → 0, ∀i /∈ E (x∗).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds For i /∈ E (x∗), we have β∗ i > 0, and thus { λk0 i zk } K′ → 0, ∀i /∈ E (x∗)

Reference 68

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This paper cites Summarizing the above analysis, we can conclude that ( x∗, λ∗) is a KKT pair of problem ( Pρ).

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds Summarizing the above analysis, we can conclude that ( x∗, λ∗) is a KKT pair of problem ( Pρ)

Reference 75

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