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A penalty-free method for equality constrained optimization
1. | School of Mathematics Science, Soochow University, Suzhou, 215006, China, China, China |
References:
[1] |
R. Andreani, E. G. Birgin, J. M. Martinez and M. L. Schuverdt, Augmented Lagrangian methods under the constant positive linear dependence constraint qualification, Math. Prog. Ser. B, 111 (2008), 5-32.
doi: 10.1007/s10107-006-0077-1. |
[2] |
R. H. Bielschowsky and F. A. M. Gomes, Dynamic control of infeasibility in equality constrained optimization, SIAM J. Optim., 19 (2008), 1299-1325.
doi: 10.1137/070679557. |
[3] |
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing enviroment, ACM Tran. Math. Software, 21 (1995), 123-160. |
[4] |
I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint, "A Numerical Comparison between the LANCELOT and MINOS Packages for Large-Scale Constrained Optimization: The Complete Numerical Results," Report 97/14, Departement de Mathematique, Faculties Universitaires de Namur, 1997. |
[5] |
R. H. Byrd, F. E. Curtis and J. Nocedal, An inexact SQP method for equality constrained optimization, SIAM J Optim., 19 (2008), 351-369.
doi: 10.1137/060674004. |
[6] |
R. H. Byrd, F. E. Curtis and J. Nocedal, An inexact Newton method for nonconvex equality constrained optimization, Math. Prog., 122 (2010), 273-299.
doi: 10.1007/s10107-008-0248-3. |
[7] |
Z. W. Chen, A penalty-free-type nonmonotone trust-region method for nonlinear constrained optimization, Appl. Math. and Comput., 173 (2006), 1014-1046.
doi: 10.1016/j.amc.2005.04.031. |
[8] |
C. M. Chin and R. Fletcher, On the global convergence of an SLP-filter algorithm that takes EQP steps, Math. Prog. Ser. A, 96 (2003), 161-177. |
[9] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods," MPS-SIAM Ser. Optim., SIAM, Philadelphia, PA, Mathematical Programming Society (MPS), Philadelphia, PA, 2000.
doi: 10.1137/1.9780898719857. |
[10] |
E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Math. Prog. Serial A., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[11] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Prog. Ser. A, 91 (2002), 239-269.
doi: 10.1007/s101070100244. |
[12] |
R. Fletcher, S. Leyffer and Ph. L. Toint, On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13 (2002), 44-59.
doi: 10.1137/S105262340038081X. |
[13] |
R. Fletcher, S. Leyffer and Ph. L. Toint, "A Brief History of Filter Methods," Optimization Online, September 26, 2006. |
[14] |
N. I. M. Gould and Ph. L. Toint, Nonlinear programming without a penalty function or a filter, Math. Prog. Ser. A, 122 (2010), 155-196.
doi: 10.1007/s10107-008-0244-7. |
[15] |
X. Liu and Y. Yuan, A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization, SIAM J. Optim., 21 (2011), 545-571.
doi: 10.1137/080739884. |
[16] |
S. Qiu and Z. Chen, A new penalty-free-type algorithm that based on trust region techniques, Appl. Math. Comput., 218 (2012), 11089-11099.
doi: 10.1016/j.amc.2012.04.065. |
[17] |
M. Ulbrich and S. Ulbrich, Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Prog. Ser. B, 95 (2003), 103-135.
doi: 10.1007/s10107-002-0343-9. |
[18] |
M. Ulbrich, S. Ulbrich and L. N. Vicente, A globally convergent primal-dual interior-point filter method for nonlinear programming, Math. Prog. Ser. A, 100 (2004), 379-410.
doi: 10.1007/s10107-003-0477-4. |
[19] |
A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim., 16 (2005), 32-48.
doi: 10.1137/S1052623403426544. |
[20] |
H. Yamashita, "A Globally Convergent Quasi-Newton Method for Equality Constrained Optimization that Does Not Use a Penalty Function," Technical Report, Mathematical System Inc., Tokyo, Japan, June 1979 (revised September 1982). |
[21] |
H. Yamashita and H. Yabe, "A Globally and Superlinearly Convergent Trust-Region SQP Method Without a Penalty Function for Nonlinearly Constrained Optimization," Technical Report, Mathematical System Inc., Tokyo, Japan, September 2003 (revised July 2007). |
[22] |
C. Zoppke-Donaldson, "A Tolerance Tube Approach to Sequential Quadratic Programming with Applications," Ph.D Thesis, Department of Mathematics and Computer Science, University of Dundee, Dundee, Scotland, UK, 1995. |
show all references
References:
[1] |
R. Andreani, E. G. Birgin, J. M. Martinez and M. L. Schuverdt, Augmented Lagrangian methods under the constant positive linear dependence constraint qualification, Math. Prog. Ser. B, 111 (2008), 5-32.
doi: 10.1007/s10107-006-0077-1. |
[2] |
R. H. Bielschowsky and F. A. M. Gomes, Dynamic control of infeasibility in equality constrained optimization, SIAM J. Optim., 19 (2008), 1299-1325.
doi: 10.1137/070679557. |
[3] |
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing enviroment, ACM Tran. Math. Software, 21 (1995), 123-160. |
[4] |
I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint, "A Numerical Comparison between the LANCELOT and MINOS Packages for Large-Scale Constrained Optimization: The Complete Numerical Results," Report 97/14, Departement de Mathematique, Faculties Universitaires de Namur, 1997. |
[5] |
R. H. Byrd, F. E. Curtis and J. Nocedal, An inexact SQP method for equality constrained optimization, SIAM J Optim., 19 (2008), 351-369.
doi: 10.1137/060674004. |
[6] |
R. H. Byrd, F. E. Curtis and J. Nocedal, An inexact Newton method for nonconvex equality constrained optimization, Math. Prog., 122 (2010), 273-299.
doi: 10.1007/s10107-008-0248-3. |
[7] |
Z. W. Chen, A penalty-free-type nonmonotone trust-region method for nonlinear constrained optimization, Appl. Math. and Comput., 173 (2006), 1014-1046.
doi: 10.1016/j.amc.2005.04.031. |
[8] |
C. M. Chin and R. Fletcher, On the global convergence of an SLP-filter algorithm that takes EQP steps, Math. Prog. Ser. A, 96 (2003), 161-177. |
[9] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods," MPS-SIAM Ser. Optim., SIAM, Philadelphia, PA, Mathematical Programming Society (MPS), Philadelphia, PA, 2000.
doi: 10.1137/1.9780898719857. |
[10] |
E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Math. Prog. Serial A., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[11] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Prog. Ser. A, 91 (2002), 239-269.
doi: 10.1007/s101070100244. |
[12] |
R. Fletcher, S. Leyffer and Ph. L. Toint, On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13 (2002), 44-59.
doi: 10.1137/S105262340038081X. |
[13] |
R. Fletcher, S. Leyffer and Ph. L. Toint, "A Brief History of Filter Methods," Optimization Online, September 26, 2006. |
[14] |
N. I. M. Gould and Ph. L. Toint, Nonlinear programming without a penalty function or a filter, Math. Prog. Ser. A, 122 (2010), 155-196.
doi: 10.1007/s10107-008-0244-7. |
[15] |
X. Liu and Y. Yuan, A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization, SIAM J. Optim., 21 (2011), 545-571.
doi: 10.1137/080739884. |
[16] |
S. Qiu and Z. Chen, A new penalty-free-type algorithm that based on trust region techniques, Appl. Math. Comput., 218 (2012), 11089-11099.
doi: 10.1016/j.amc.2012.04.065. |
[17] |
M. Ulbrich and S. Ulbrich, Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Prog. Ser. B, 95 (2003), 103-135.
doi: 10.1007/s10107-002-0343-9. |
[18] |
M. Ulbrich, S. Ulbrich and L. N. Vicente, A globally convergent primal-dual interior-point filter method for nonlinear programming, Math. Prog. Ser. A, 100 (2004), 379-410.
doi: 10.1007/s10107-003-0477-4. |
[19] |
A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim., 16 (2005), 32-48.
doi: 10.1137/S1052623403426544. |
[20] |
H. Yamashita, "A Globally Convergent Quasi-Newton Method for Equality Constrained Optimization that Does Not Use a Penalty Function," Technical Report, Mathematical System Inc., Tokyo, Japan, June 1979 (revised September 1982). |
[21] |
H. Yamashita and H. Yabe, "A Globally and Superlinearly Convergent Trust-Region SQP Method Without a Penalty Function for Nonlinearly Constrained Optimization," Technical Report, Mathematical System Inc., Tokyo, Japan, September 2003 (revised July 2007). |
[22] |
C. Zoppke-Donaldson, "A Tolerance Tube Approach to Sequential Quadratic Programming with Applications," Ph.D Thesis, Department of Mathematics and Computer Science, University of Dundee, Dundee, Scotland, UK, 1995. |
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