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Two approaches for solving mathematical programs with second-order cone complementarity constraints
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China |
2. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning |
3. | School of Management, Shanghai University, Shanghai 200444, China |
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, 95 (2003), 3-51.
doi: 10.1007/s10107-002-0339-5. |
[2] |
J. S. Chen, X. Chen and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second-order cones, Mathematical Programming, 101 (2004), 95-117.
doi: 10.1007/s10107-004-0538-3. |
[3] |
J. S. Chen and S. Pan, A survey on SOC complementarity functions and solution methods for SOCPs and SOCCPs, Pacific Journal of Optimization, 8 (2012), 33-74. |
[4] |
X. D. Chen, D. Sun and J. Sun, Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems, Computational Optimization and Applications, 25 (2003), 39-56.
doi: 10.1023/A:1022996819381. |
[5] |
Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193-209.
doi: 10.1080/02331939508844048. |
[6] |
U. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Mathematical Monographs, Oxford University Press, New York, 1994. |
[7] |
M. Fukushima and G. H. Lin, Smoothing methods for mathematical programs with equilibrium constraints, Proceedings of the ICKS'04, IEEE Computer Society, 2004 (2004), 206-213.
doi: 10.1109/ICKS.2004.1313426. |
[8] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order cone complementarity problems, SIAM Journal on Optimization, 12 (2001), 436-460.
doi: 10.1137/S1052623400380365. |
[9] |
S. Hayashi, N. Yamashita and M. Fukushima, A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM Journal on Optimization, 15 (2005), 593-615.
doi: 10.1137/S1052623403421516. |
[10] |
Y. C. Liang, X. D. Zhu and G. H. Lin, Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints, Set-Valued and Variational Analysis, 22 (2014), 59-78.
doi: 10.1007/s11228-013-0250-7. |
[11] |
Z. Q. Luo, J. S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, United Kingdom, 1996.
doi: 10.1017/CBO9780511983658. |
[12] |
J. Outrata, M. Kocvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equlilibrium Constraints: Theory, Applications, and Numerical Results, Kluwer Academic Publisher, Dordrect, The Netherlands, 1998.
doi: 10.1007/978-1-4757-2825-5. |
[13] |
J. V. Outrata and D. F. Sun, On the coderivative of the projection operator onto the second order cone, Set-Valued Analysis, 16 (2008), 999-1014.
doi: 10.1007/s11228-008-0092-x. |
[14] |
T. Yan and M. Fukushima, Smoothing method for mathematical programs with symmetric cone complementarity, Optimization, 60 (2011), 113-128.
doi: 10.1080/02331934.2010.541458. |
[15] |
H. Yamamura, T. Okuno, S. Hayashi and M. Fukushima, A smoothing SQP method for mathematical programs with linear second-order cone complementarity constraints, Pacific Journal of Optimization, 9 (2013), 345-372. |
[16] |
J. J. Ye, D. L. Zhu and Q. J. Zhu, Exact penalization and neccessary conditions for generalized bilevel programming problems, SIAM Journal on Optimizaion, 7 (1997), 481-507.
doi: 10.1137/S1052623493257344. |
[17] |
Y. Zhang, L. Zhang and J. Wu, Convergence properties of a smoothing approach for mathematical programs with second-order cone complementarity constraints, Set-Valued Analysis, 19 (2011), 609-646.
doi: 10.1007/s11228-011-0190-z. |
show all references
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, 95 (2003), 3-51.
doi: 10.1007/s10107-002-0339-5. |
[2] |
J. S. Chen, X. Chen and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second-order cones, Mathematical Programming, 101 (2004), 95-117.
doi: 10.1007/s10107-004-0538-3. |
[3] |
J. S. Chen and S. Pan, A survey on SOC complementarity functions and solution methods for SOCPs and SOCCPs, Pacific Journal of Optimization, 8 (2012), 33-74. |
[4] |
X. D. Chen, D. Sun and J. Sun, Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems, Computational Optimization and Applications, 25 (2003), 39-56.
doi: 10.1023/A:1022996819381. |
[5] |
Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193-209.
doi: 10.1080/02331939508844048. |
[6] |
U. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Mathematical Monographs, Oxford University Press, New York, 1994. |
[7] |
M. Fukushima and G. H. Lin, Smoothing methods for mathematical programs with equilibrium constraints, Proceedings of the ICKS'04, IEEE Computer Society, 2004 (2004), 206-213.
doi: 10.1109/ICKS.2004.1313426. |
[8] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order cone complementarity problems, SIAM Journal on Optimization, 12 (2001), 436-460.
doi: 10.1137/S1052623400380365. |
[9] |
S. Hayashi, N. Yamashita and M. Fukushima, A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM Journal on Optimization, 15 (2005), 593-615.
doi: 10.1137/S1052623403421516. |
[10] |
Y. C. Liang, X. D. Zhu and G. H. Lin, Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints, Set-Valued and Variational Analysis, 22 (2014), 59-78.
doi: 10.1007/s11228-013-0250-7. |
[11] |
Z. Q. Luo, J. S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, United Kingdom, 1996.
doi: 10.1017/CBO9780511983658. |
[12] |
J. Outrata, M. Kocvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equlilibrium Constraints: Theory, Applications, and Numerical Results, Kluwer Academic Publisher, Dordrect, The Netherlands, 1998.
doi: 10.1007/978-1-4757-2825-5. |
[13] |
J. V. Outrata and D. F. Sun, On the coderivative of the projection operator onto the second order cone, Set-Valued Analysis, 16 (2008), 999-1014.
doi: 10.1007/s11228-008-0092-x. |
[14] |
T. Yan and M. Fukushima, Smoothing method for mathematical programs with symmetric cone complementarity, Optimization, 60 (2011), 113-128.
doi: 10.1080/02331934.2010.541458. |
[15] |
H. Yamamura, T. Okuno, S. Hayashi and M. Fukushima, A smoothing SQP method for mathematical programs with linear second-order cone complementarity constraints, Pacific Journal of Optimization, 9 (2013), 345-372. |
[16] |
J. J. Ye, D. L. Zhu and Q. J. Zhu, Exact penalization and neccessary conditions for generalized bilevel programming problems, SIAM Journal on Optimizaion, 7 (1997), 481-507.
doi: 10.1137/S1052623493257344. |
[17] |
Y. Zhang, L. Zhang and J. Wu, Convergence properties of a smoothing approach for mathematical programs with second-order cone complementarity constraints, Set-Valued Analysis, 19 (2011), 609-646.
doi: 10.1007/s11228-011-0190-z. |
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