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A penaltyfree 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), 532. doi: 10.1007/s1010700600771. 
[2] 
R. H. Bielschowsky and F. A. M. Gomes, Dynamic control of infeasibility in equality constrained optimization, SIAM J. Optim., 19 (2008), 12991325. 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), 123160. 
[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 LargeScale 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), 351369. 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), 273299. doi: 10.1007/s1010700802483. 
[7] 
Z. W. Chen, A penaltyfreetype nonmonotone trustregion method for nonlinear constrained optimization, Appl. Math. and Comput., 173 (2006), 10141046. doi: 10.1016/j.amc.2005.04.031. 
[8] 
C. M. Chin and R. Fletcher, On the global convergence of an SLPfilter algorithm that takes EQP steps, Math. Prog. Ser. A, 96 (2003), 161177. 
[9] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods," MPSSIAM 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), 201213. doi: 10.1007/s101070100263. 
[11] 
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Prog. Ser. A, 91 (2002), 239269. doi: 10.1007/s101070100244. 
[12] 
R. Fletcher, S. Leyffer and Ph. L. Toint, On the global convergence of a filterSQP algorithm, SIAM J. Optim., 13 (2002), 4459. 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), 155196. doi: 10.1007/s1010700802447. 
[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), 545571. doi: 10.1137/080739884. 
[16] 
S. Qiu and Z. Chen, A new penaltyfreetype algorithm that based on trust region techniques, Appl. Math. Comput., 218 (2012), 1108911099. doi: 10.1016/j.amc.2012.04.065. 
[17] 
M. Ulbrich and S. Ulbrich, Nonmonotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Prog. Ser. B, 95 (2003), 103135. doi: 10.1007/s1010700203439. 
[18] 
M. Ulbrich, S. Ulbrich and L. N. Vicente, A globally convergent primaldual interiorpoint filter method for nonlinear programming, Math. Prog. Ser. A, 100 (2004), 379410. doi: 10.1007/s1010700304774. 
[19] 
A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim., 16 (2005), 3248. doi: 10.1137/S1052623403426544. 
[20] 
H. Yamashita, "A Globally Convergent QuasiNewton 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 TrustRegion SQP Method Without a Penalty Function for Nonlinearly Constrained Optimization," Technical Report, Mathematical System Inc., Tokyo, Japan, September 2003 (revised July 2007). 
[22] 
C. ZoppkeDonaldson, "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), 532. doi: 10.1007/s1010700600771. 
[2] 
R. H. Bielschowsky and F. A. M. Gomes, Dynamic control of infeasibility in equality constrained optimization, SIAM J. Optim., 19 (2008), 12991325. 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), 123160. 
[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 LargeScale 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), 351369. 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), 273299. doi: 10.1007/s1010700802483. 
[7] 
Z. W. Chen, A penaltyfreetype nonmonotone trustregion method for nonlinear constrained optimization, Appl. Math. and Comput., 173 (2006), 10141046. doi: 10.1016/j.amc.2005.04.031. 
[8] 
C. M. Chin and R. Fletcher, On the global convergence of an SLPfilter algorithm that takes EQP steps, Math. Prog. Ser. A, 96 (2003), 161177. 
[9] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods," MPSSIAM 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), 201213. doi: 10.1007/s101070100263. 
[11] 
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Prog. Ser. A, 91 (2002), 239269. doi: 10.1007/s101070100244. 
[12] 
R. Fletcher, S. Leyffer and Ph. L. Toint, On the global convergence of a filterSQP algorithm, SIAM J. Optim., 13 (2002), 4459. 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), 155196. doi: 10.1007/s1010700802447. 
[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), 545571. doi: 10.1137/080739884. 
[16] 
S. Qiu and Z. Chen, A new penaltyfreetype algorithm that based on trust region techniques, Appl. Math. Comput., 218 (2012), 1108911099. doi: 10.1016/j.amc.2012.04.065. 
[17] 
M. Ulbrich and S. Ulbrich, Nonmonotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Prog. Ser. B, 95 (2003), 103135. doi: 10.1007/s1010700203439. 
[18] 
M. Ulbrich, S. Ulbrich and L. N. Vicente, A globally convergent primaldual interiorpoint filter method for nonlinear programming, Math. Prog. Ser. A, 100 (2004), 379410. doi: 10.1007/s1010700304774. 
[19] 
A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim., 16 (2005), 3248. doi: 10.1137/S1052623403426544. 
[20] 
H. Yamashita, "A Globally Convergent QuasiNewton 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 TrustRegion SQP Method Without a Penalty Function for Nonlinearly Constrained Optimization," Technical Report, Mathematical System Inc., Tokyo, Japan, September 2003 (revised July 2007). 
[22] 
C. ZoppkeDonaldson, "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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