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A smooth QP-free algorithm without a penalty function or a filter for mathematical programs with complementarity constraints
1. | College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China, China, China |
References:
[1] |
R. W. Cottle, J. S. Pang and R. E. Stone, The Linear Complementarity Problem,, Academic Press: Boston, (1992).
|
[2] |
F. Facchinei, H. Y. Jiang and L. Q. Qi, A smoothing method for mathematical programs with equilibrium constraints,, Math. Program, 85 (1999), 107.
doi: 10.1007/s101070050048. |
[3] |
M. Fukushima, Z. Q. Luo and J. S. Pang, A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints,, Comput. Optim. Appl., 10 (1998), 5.
doi: 10.1023/A:1018359900133. |
[4] |
Z. Y. Gao, G. P. He and F. Wu, A sequential systems of linear equations method with arbitrary initial point,, SCI China Ser A, 27 (1997), 24.
doi: 10.1007/BF02876059. |
[5] |
Z. Y. Gao, G. P. He and F. Wu, Sequential systems of linear equations algorithm for nonlinear optimization problems with general constraints,, J. Optimi. Theory Appl., 95 (1997), 371.
doi: 10.1023/A:1022639306130. |
[6] |
H. W. Ge and Z. W. Chen, A penalty-free method with line search for nonlinear equality constrained optimization,, Appl. Math. Model., 37 (2013), 9934.
doi: 10.1016/j.apm.2013.05.037. |
[7] |
J. B. Jian, A superlinearly convergent implicit smooth SQP algorithm for mathematical programs with nonlinear complementarity constraints,, Comput. Optim. Appl., 31 (2005), 335.
doi: 10.1007/s10589-005-3230-5. |
[8] |
J. B. Jian, J. L. Li and X. D. Mo, A strongly and superlinearly convergent SQP algorithm for optimization problems with linear complementarity constraints,, Appl. Math. Optim., 54 (2006), 17.
doi: 10.1007/s00245-005-0848-8. |
[9] |
J. B. Jian, Fast Algorithms for Smooth Constrained Optimization: Theoretical Analysis and Numerical Experiments,, Science Press, (2010). Google Scholar |
[10] |
H. Y. Jiang and D. Ralph, Smooth SQP methods for mathematical programs with nonlinear complementarity constraints,, SIAM J. Optim., 10 (2000), 779.
doi: 10.1137/S1052623497332329. |
[11] |
A. Kadrani, J. P Dussault and A. Benchakroun, A new regularization scheme for mathematical programs with complementarity constraints,, SIAM J. Optim., 20 (2009), 78.
doi: 10.1137/070705490. |
[12] |
C. Kanzow, Some noninterior continuation methods for linear complementarity problems,, SIAM J. Matrix Anal., 17 (1996), 851.
doi: 10.1137/S0895479894273134. |
[13] |
J. L. Li and J. B. Jian, A superlinearly convergent SSLE algorithm for optimization problems with linear complementarity constraints,, J. Global Optim., 33 (2005), 477.
doi: 10.1007/s10898-004-2708-5. |
[14] |
G. H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints,, Ann. Oper. Res., 133 (2005), 63.
doi: 10.1007/s10479-004-5024-z. |
[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.
doi: 10.1137/080739884. |
[16] |
W. A. Liu, C. G. Shen, X. J. Zhu and D. G. Pu, An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality constrained optimization,, Optim. Method Softw., 29 (2014), 1238.
doi: 10.1080/10556788.2013.879587. |
[17] |
Z. Q. Luo, J. S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints,, Cambridge University Press, (1996).
doi: 10.1017/CBO9780511983658. |
[18] |
H. Z. Luo, X. L. Sun and Y. F. Xu, Convergence properties of modified partially augmented Lagrangian methods for mathematical programs with complementarity constraints,, J. Optimi. Theory Appl., 145 (2010), 489.
doi: 10.1007/s10957-009-9642-0. |
[19] |
H. Z. Luo, X. L. Sun, Y. F. Xu and H. X. Wu, On the convergence properties of modified augmented lagrangian methods for Mathematical Programming with Complementarity Constraints,, J. Global Optim, 46 (2010), 217.
doi: 10.1007/s10898-009-9419-x. |
[20] |
J. Outrata, M. Kocvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results,, Springer, (1998).
doi: 10.1007/978-1-4757-2825-5. |
[21] |
E. R. Panier, A. L. Tits and J. N. Herskovits, A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,, SIAM J. Optim., 26 (1988), 788.
doi: 10.1137/0326046. |
[22] |
H. D. Qi and L. Q. Qi, A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,, SIAM J. Optimi., 11 (2000), 113.
doi: 10.1137/S1052623499353935. |
[23] |
Hoheisel Tim, Kanzow Christian and Schwartz Alexandra, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints,, Math. Program., 137 (2013), 257.
doi: 10.1007/s10107-011-0488-5. |
[24] |
Y. F. Yang, D. H. Li and L. Q. Qi, A feasible sequential linear equation method for inequality constrained optimization,, SIAM J. Optim., 13 (2003), 1222.
doi: 10.1137/S1052623401383881. |
[25] |
Z. B. Zhu and K. C. Zhang, A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints,, \emph{Appl. Math. Comput.}, 172 (2006), 222.
doi: 10.1016/j.amc.2005.01.141. |
show all references
References:
[1] |
R. W. Cottle, J. S. Pang and R. E. Stone, The Linear Complementarity Problem,, Academic Press: Boston, (1992).
|
[2] |
F. Facchinei, H. Y. Jiang and L. Q. Qi, A smoothing method for mathematical programs with equilibrium constraints,, Math. Program, 85 (1999), 107.
doi: 10.1007/s101070050048. |
[3] |
M. Fukushima, Z. Q. Luo and J. S. Pang, A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints,, Comput. Optim. Appl., 10 (1998), 5.
doi: 10.1023/A:1018359900133. |
[4] |
Z. Y. Gao, G. P. He and F. Wu, A sequential systems of linear equations method with arbitrary initial point,, SCI China Ser A, 27 (1997), 24.
doi: 10.1007/BF02876059. |
[5] |
Z. Y. Gao, G. P. He and F. Wu, Sequential systems of linear equations algorithm for nonlinear optimization problems with general constraints,, J. Optimi. Theory Appl., 95 (1997), 371.
doi: 10.1023/A:1022639306130. |
[6] |
H. W. Ge and Z. W. Chen, A penalty-free method with line search for nonlinear equality constrained optimization,, Appl. Math. Model., 37 (2013), 9934.
doi: 10.1016/j.apm.2013.05.037. |
[7] |
J. B. Jian, A superlinearly convergent implicit smooth SQP algorithm for mathematical programs with nonlinear complementarity constraints,, Comput. Optim. Appl., 31 (2005), 335.
doi: 10.1007/s10589-005-3230-5. |
[8] |
J. B. Jian, J. L. Li and X. D. Mo, A strongly and superlinearly convergent SQP algorithm for optimization problems with linear complementarity constraints,, Appl. Math. Optim., 54 (2006), 17.
doi: 10.1007/s00245-005-0848-8. |
[9] |
J. B. Jian, Fast Algorithms for Smooth Constrained Optimization: Theoretical Analysis and Numerical Experiments,, Science Press, (2010). Google Scholar |
[10] |
H. Y. Jiang and D. Ralph, Smooth SQP methods for mathematical programs with nonlinear complementarity constraints,, SIAM J. Optim., 10 (2000), 779.
doi: 10.1137/S1052623497332329. |
[11] |
A. Kadrani, J. P Dussault and A. Benchakroun, A new regularization scheme for mathematical programs with complementarity constraints,, SIAM J. Optim., 20 (2009), 78.
doi: 10.1137/070705490. |
[12] |
C. Kanzow, Some noninterior continuation methods for linear complementarity problems,, SIAM J. Matrix Anal., 17 (1996), 851.
doi: 10.1137/S0895479894273134. |
[13] |
J. L. Li and J. B. Jian, A superlinearly convergent SSLE algorithm for optimization problems with linear complementarity constraints,, J. Global Optim., 33 (2005), 477.
doi: 10.1007/s10898-004-2708-5. |
[14] |
G. H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints,, Ann. Oper. Res., 133 (2005), 63.
doi: 10.1007/s10479-004-5024-z. |
[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.
doi: 10.1137/080739884. |
[16] |
W. A. Liu, C. G. Shen, X. J. Zhu and D. G. Pu, An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality constrained optimization,, Optim. Method Softw., 29 (2014), 1238.
doi: 10.1080/10556788.2013.879587. |
[17] |
Z. Q. Luo, J. S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints,, Cambridge University Press, (1996).
doi: 10.1017/CBO9780511983658. |
[18] |
H. Z. Luo, X. L. Sun and Y. F. Xu, Convergence properties of modified partially augmented Lagrangian methods for mathematical programs with complementarity constraints,, J. Optimi. Theory Appl., 145 (2010), 489.
doi: 10.1007/s10957-009-9642-0. |
[19] |
H. Z. Luo, X. L. Sun, Y. F. Xu and H. X. Wu, On the convergence properties of modified augmented lagrangian methods for Mathematical Programming with Complementarity Constraints,, J. Global Optim, 46 (2010), 217.
doi: 10.1007/s10898-009-9419-x. |
[20] |
J. Outrata, M. Kocvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results,, Springer, (1998).
doi: 10.1007/978-1-4757-2825-5. |
[21] |
E. R. Panier, A. L. Tits and J. N. Herskovits, A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,, SIAM J. Optim., 26 (1988), 788.
doi: 10.1137/0326046. |
[22] |
H. D. Qi and L. Q. Qi, A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,, SIAM J. Optimi., 11 (2000), 113.
doi: 10.1137/S1052623499353935. |
[23] |
Hoheisel Tim, Kanzow Christian and Schwartz Alexandra, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints,, Math. Program., 137 (2013), 257.
doi: 10.1007/s10107-011-0488-5. |
[24] |
Y. F. Yang, D. H. Li and L. Q. Qi, A feasible sequential linear equation method for inequality constrained optimization,, SIAM J. Optim., 13 (2003), 1222.
doi: 10.1137/S1052623401383881. |
[25] |
Z. B. Zhu and K. C. Zhang, A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints,, \emph{Appl. Math. Comput.}, 172 (2006), 222.
doi: 10.1016/j.amc.2005.01.141. |
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