-
Previous Article
On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach
- JIMO Home
- This Issue
-
Next Article
American type geometric step options
A log-exponential regularization method for a mathematical program with general vertical complementarity constraints
1. | School of Mathematics, Liaoning Normal University, Dalian, 116029, China |
2. | School of information Science and Engineering, Dalian Polytechnic University, Dalian, 116029, China, China |
References:
[1] |
S. I. Birbil, G. Gürkan and O. Listes, Solving stochastic mathematical programs with complementarity constraints using simulation,, Math. Oper. Res., 31 (2006), 739.
doi: 10.1287/moor.1060.0215. |
[2] |
R. W. Cottle and G. B. Dantzig, A generalization of the linear complementarity problem,, J. Combinatorial Theory, 8 (1970), 79.
doi: 10.1016/S0021-9800(70)80010-2. |
[3] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", John Wiley and Sons, (1983).
|
[4] |
M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints,, in, (1999), 99.
doi: 10.1007/978-3-642-45780-7_7. |
[5] |
A. Fischer, A special Newton-type optimization method,, Optimization, 24 (1992), 269.
doi: 10.1080/02331939208843795. |
[6] |
M. S. Gowda and R. Sznajder, A generalization of the Nash equilibrium theorem on bimatrix games,, International Journal of Game Theory, 25 (1996), 1.
doi: 10.1007/BF01254380. |
[7] |
Z. Huang and J. Sun, A smoothing Newton algorithm for mathematical programs with complementarity constraints,, Journal of Industrial and Management Optimization, 1 (2005), 153.
doi: 10.3934/jimo.2005.1.153. |
[8] |
X. Liu and J. Sun, Generalized stationary points and an interior point method for mathematical programs with equilibrium constraints,, Mathematical Programming, 101 (2004), 231.
doi: 10.1007/s10107-004-0543-6. |
[9] |
X. Liu, G. Perakis and J. Sun, A robust SQP method for mathematical programs with linear complementarity constraints,, Computational Optimization and Applications, 34 (2006), 5.
doi: 10.1007/s10589-005-3075-y. |
[10] |
Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints,", Cambridge University Press, (1996).
doi: 10.1017/CBO9780511983658. |
[11] |
M. Kočvara and J. V. Outrata, Optimization problems with equilibrium constraints and their numerical solution,, Math. Program., 101 (2004), 119.
doi: 10.1007/s10107-004-0539-2. |
[12] |
J. Peng and Z. Lin, A non-interior continuation method for generalized linear complementarity problems,, Mathematical Programming, 86 (1999), 533.
doi: 10.1007/s101070050104. |
[13] |
H. Qi and L. Liao, A smoothing Newton method for extended vertical linear complementarity problems,, SIAM Joural of Matrix Analysis and Applications, 21 (1999), 45.
doi: 10.1137/S0895479897329837. |
[14] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis,", Berlin Heidelberg, (1998).
doi: 10.1007/978-3-642-02431-3. |
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stability, optimality, and sensitivity,, Math. Oper. Res., 25 (2000), 1.
doi: 10.1287/moor.25.1.1.15213. |
[17] |
H. V. Stackelberg, "The Theory of Market Economy,", Oxford University Press, (1952). Google Scholar |
[18] |
H. Yin and J. Zhang, Global convergence of a smooth approximation method for mathematical programs with complementarity constraints,, Math. Meth. Oper. Res., 64 (2006), 255.
doi: 10.1007/s00186-006-0076-2. |
[19] |
N. D. Yen, Stability of the solution set of perturbed nonsmooth inequality systems and application,, Journal of Optimization Theory and Applications, 93 (1997), 199.
doi: 10.1023/A:1022662120550. |
[20] |
J. Zhang, L. Zhang and S. Lin, A class of smoothing SAA methods for a stochastic mathematical program with complementarity constraints,, J. Math. Anal. Appl., 387 (2012), 201.
doi: 10.1016/j.jmaa.2011.08.073. |
[21] |
J. Zhang, L. Zhang and W. Wang, On constraint qualifications in terms of approximate Jacobians for nonsmooth continuous optimization problems,, Nonlinear Analysis, 75 (2012), 2566.
doi: 10.1016/j.na.2011.11.003. |
show all references
References:
[1] |
S. I. Birbil, G. Gürkan and O. Listes, Solving stochastic mathematical programs with complementarity constraints using simulation,, Math. Oper. Res., 31 (2006), 739.
doi: 10.1287/moor.1060.0215. |
[2] |
R. W. Cottle and G. B. Dantzig, A generalization of the linear complementarity problem,, J. Combinatorial Theory, 8 (1970), 79.
doi: 10.1016/S0021-9800(70)80010-2. |
[3] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", John Wiley and Sons, (1983).
|
[4] |
M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints,, in, (1999), 99.
doi: 10.1007/978-3-642-45780-7_7. |
[5] |
A. Fischer, A special Newton-type optimization method,, Optimization, 24 (1992), 269.
doi: 10.1080/02331939208843795. |
[6] |
M. S. Gowda and R. Sznajder, A generalization of the Nash equilibrium theorem on bimatrix games,, International Journal of Game Theory, 25 (1996), 1.
doi: 10.1007/BF01254380. |
[7] |
Z. Huang and J. Sun, A smoothing Newton algorithm for mathematical programs with complementarity constraints,, Journal of Industrial and Management Optimization, 1 (2005), 153.
doi: 10.3934/jimo.2005.1.153. |
[8] |
X. Liu and J. Sun, Generalized stationary points and an interior point method for mathematical programs with equilibrium constraints,, Mathematical Programming, 101 (2004), 231.
doi: 10.1007/s10107-004-0543-6. |
[9] |
X. Liu, G. Perakis and J. Sun, A robust SQP method for mathematical programs with linear complementarity constraints,, Computational Optimization and Applications, 34 (2006), 5.
doi: 10.1007/s10589-005-3075-y. |
[10] |
Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints,", Cambridge University Press, (1996).
doi: 10.1017/CBO9780511983658. |
[11] |
M. Kočvara and J. V. Outrata, Optimization problems with equilibrium constraints and their numerical solution,, Math. Program., 101 (2004), 119.
doi: 10.1007/s10107-004-0539-2. |
[12] |
J. Peng and Z. Lin, A non-interior continuation method for generalized linear complementarity problems,, Mathematical Programming, 86 (1999), 533.
doi: 10.1007/s101070050104. |
[13] |
H. Qi and L. Liao, A smoothing Newton method for extended vertical linear complementarity problems,, SIAM Joural of Matrix Analysis and Applications, 21 (1999), 45.
doi: 10.1137/S0895479897329837. |
[14] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis,", Berlin Heidelberg, (1998).
doi: 10.1007/978-3-642-02431-3. |
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stability, optimality, and sensitivity,, Math. Oper. Res., 25 (2000), 1.
doi: 10.1287/moor.25.1.1.15213. |
[17] |
H. V. Stackelberg, "The Theory of Market Economy,", Oxford University Press, (1952). Google Scholar |
[18] |
H. Yin and J. Zhang, Global convergence of a smooth approximation method for mathematical programs with complementarity constraints,, Math. Meth. Oper. Res., 64 (2006), 255.
doi: 10.1007/s00186-006-0076-2. |
[19] |
N. D. Yen, Stability of the solution set of perturbed nonsmooth inequality systems and application,, Journal of Optimization Theory and Applications, 93 (1997), 199.
doi: 10.1023/A:1022662120550. |
[20] |
J. Zhang, L. Zhang and S. Lin, A class of smoothing SAA methods for a stochastic mathematical program with complementarity constraints,, J. Math. Anal. Appl., 387 (2012), 201.
doi: 10.1016/j.jmaa.2011.08.073. |
[21] |
J. Zhang, L. Zhang and W. Wang, On constraint qualifications in terms of approximate Jacobians for nonsmooth continuous optimization problems,, Nonlinear Analysis, 75 (2012), 2566.
doi: 10.1016/j.na.2011.11.003. |
[1] |
David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002 |
[2] |
Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565 |
[3] |
Ralf Hielscher, Michael Quellmalz. Reconstructing a function on the sphere from its means along vertical slices. Inverse Problems & Imaging, 2016, 10 (3) : 711-739. doi: 10.3934/ipi.2016018 |
[4] |
Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 |
[5] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
[6] |
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 |
[7] |
Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013 |
[8] |
Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 |
[9] |
Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192 |
[10] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
[11] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[12] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]