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Globally convergent algorithm for solving stationary points for mathematical programs with complementarity constraints via nonsmooth reformulations
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China |
2. | School of Management, Shanghai University, Shanghai 200444, China |
References:
[1] |
D. P. Bertsekas, "Nonlinear Programming," $2^{nd}$ edition, Athena Scientific, Belmont, Massachusetts, 1999. |
[2] |
F. Facchinei and J. Soares, A new merit function for nonlinear complementarity problems and a related algorithm, SIAM J. Optim., 7 (1997), 225-247.
doi: 10.1137/S1052623494279110. |
[3] |
A. Fischer, A special Newton-type optimization method, Optim., 24 (1992), 269-284.
doi: 10.1080/02331939208843795. |
[4] |
M. L. Flegel and C. Kanzow, Abadie-type constraint qualification for mathematical programs with equilibrium constraints, J. Optim. Theory Appl., 124 (2005), 595-614.
doi: 10.1007/s10957-004-1176-x. |
[5] |
R. Fletcher, S. Leyffer, D. Ralph and S. Scholtes, Local convergence of SQP methods for mathematical programs with equilibrium constraints, SIAM J. Optim., 17 (2006), 259-286.
doi: 10.1137/S1052623402407382. |
[6] |
M. Fukushima and G.-H. Lin, Smoothing methods for mathematical programs with equilibrium constraints, Proceedings of the ICKS'04, IEEE Computer Society, (2004), 206-213. |
[7] |
L. Guo and G.-H. Lin, Notes on some constraint qualifications for mathematical programs with equilibrium constraints, J. Optim. Theory Appl., (2012).
doi: 10.1007/s10957-012-0084-8. |
[8] |
S. Leyffer, MacMPEC-ampl collection of mathematical programms with equilibrium constraints. Available from:, , ().
|
[9] |
G.-H. Lin, L. Guo and J.-J. Ye, Solving mathematical programs with equilibrium constraints as constrained equations,, preprint., ().
|
[10] |
T. De Luca, F. Facchinei and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems, Math. Program., 75 (1996), 407-439.
doi: 10.1016/S0025-5610(96)00028-7. |
[11] |
Z.-Q. Luo, J.-S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints," Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511983658. |
[12] |
J. V. Outrata, M. Kočvara and J. Zowe, "Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Theory, Applications and Numerical Results," Nonconvex Optimization and its Applications, 28, Kluwer Academic Publishers, Dordrecht, 1998. |
[13] |
J.-S. Pang, A B-differentiable equation-baesd, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems, Math. Program., 51 (1991), 101-131.
doi: 10.1007/BF01586928. |
[14] |
J.-S. Pang and A. Gabriel, NE/SQP: A robust algorithm for the nonlinear complementarity problem, Math. Program., 60 (1993), 295-337.
doi: 10.1007/BF01580617. |
[15] |
J.-S. Pang and L. Qi, Nonsmooth equations: Motivation and algorithm, SIAM J. Optim., 3 (1993), 443-465.
doi: 10.1137/0803021. |
[16] |
L. Qi and J. sun, A nonsmooth version of Newton's method, Math. Program., 58 (1993), 353-367.
doi: 10.1007/BF01581275. |
[17] |
P. Tseng, Growth behavior of a class of merit functions for the nonlinear complementarity problem, J. Optim. Theory Appl., 89 (1996), 17-37.
doi: 10.1007/BF02192639. |
[18] |
J. J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints, J. Math. Anal. Appl., 307 (2005), 350-369.
doi: 10.1016/j.jmaa.2004.10.032. |
show all references
References:
[1] |
D. P. Bertsekas, "Nonlinear Programming," $2^{nd}$ edition, Athena Scientific, Belmont, Massachusetts, 1999. |
[2] |
F. Facchinei and J. Soares, A new merit function for nonlinear complementarity problems and a related algorithm, SIAM J. Optim., 7 (1997), 225-247.
doi: 10.1137/S1052623494279110. |
[3] |
A. Fischer, A special Newton-type optimization method, Optim., 24 (1992), 269-284.
doi: 10.1080/02331939208843795. |
[4] |
M. L. Flegel and C. Kanzow, Abadie-type constraint qualification for mathematical programs with equilibrium constraints, J. Optim. Theory Appl., 124 (2005), 595-614.
doi: 10.1007/s10957-004-1176-x. |
[5] |
R. Fletcher, S. Leyffer, D. Ralph and S. Scholtes, Local convergence of SQP methods for mathematical programs with equilibrium constraints, SIAM J. Optim., 17 (2006), 259-286.
doi: 10.1137/S1052623402407382. |
[6] |
M. Fukushima and G.-H. Lin, Smoothing methods for mathematical programs with equilibrium constraints, Proceedings of the ICKS'04, IEEE Computer Society, (2004), 206-213. |
[7] |
L. Guo and G.-H. Lin, Notes on some constraint qualifications for mathematical programs with equilibrium constraints, J. Optim. Theory Appl., (2012).
doi: 10.1007/s10957-012-0084-8. |
[8] |
S. Leyffer, MacMPEC-ampl collection of mathematical programms with equilibrium constraints. Available from:, , ().
|
[9] |
G.-H. Lin, L. Guo and J.-J. Ye, Solving mathematical programs with equilibrium constraints as constrained equations,, preprint., ().
|
[10] |
T. De Luca, F. Facchinei and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems, Math. Program., 75 (1996), 407-439.
doi: 10.1016/S0025-5610(96)00028-7. |
[11] |
Z.-Q. Luo, J.-S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints," Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511983658. |
[12] |
J. V. Outrata, M. Kočvara and J. Zowe, "Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Theory, Applications and Numerical Results," Nonconvex Optimization and its Applications, 28, Kluwer Academic Publishers, Dordrecht, 1998. |
[13] |
J.-S. Pang, A B-differentiable equation-baesd, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems, Math. Program., 51 (1991), 101-131.
doi: 10.1007/BF01586928. |
[14] |
J.-S. Pang and A. Gabriel, NE/SQP: A robust algorithm for the nonlinear complementarity problem, Math. Program., 60 (1993), 295-337.
doi: 10.1007/BF01580617. |
[15] |
J.-S. Pang and L. Qi, Nonsmooth equations: Motivation and algorithm, SIAM J. Optim., 3 (1993), 443-465.
doi: 10.1137/0803021. |
[16] |
L. Qi and J. sun, A nonsmooth version of Newton's method, Math. Program., 58 (1993), 353-367.
doi: 10.1007/BF01581275. |
[17] |
P. Tseng, Growth behavior of a class of merit functions for the nonlinear complementarity problem, J. Optim. Theory Appl., 89 (1996), 17-37.
doi: 10.1007/BF02192639. |
[18] |
J. J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints, J. Math. Anal. Appl., 307 (2005), 350-369.
doi: 10.1016/j.jmaa.2004.10.032. |
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