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A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs
A barrier function method for generalized Nash equilibrium problems
1. | Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China |
2. | Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 |
References:
[1] |
M. Breton, G. Zaccour and M. Zahaf, A game-theoretic formulation of joint implementation of environmental projects,, European J. Oper. Res., 168 (2006), 221.
doi: 10.1016/j.ejor.2004.04.026. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis,, John Wiley, (1983).
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[3] |
J. Contreras, M. Klusch and J. B. Krawczyk, Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets,, IEEE. T. Power. Syst., 19 (2004), 195.
doi: 10.1109/TPWRS.2003.820692. |
[4] |
G. Debreu, A social equilibrium existence theorem,, Proc. Natl. Acad. Sci. U. S. A., 38 (1952), 886.
doi: 10.1073/pnas.38.10.886. |
[5] |
F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, I, (2003).
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[6] |
F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, Vol II, (2003).
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[7] |
F. Facchinei, A. Fischer and V. Piccialli, On generalized Nash games and variational inequalities,, Oper. Res. Lett., 35 (2007), 159.
doi: 10.1016/j.orl.2006.03.004. |
[8] |
F. Facchinei, A. Fischer and C. Kanzow, Regularity properties of a semismooth reformulation of variational inequalities,, SIAM J. Optim., 8 (1998), 850.
doi: 10.1137/S1052623496298194. |
[9] |
F. Facchinei, A. Fischer and V. Piccialli, Generalized Nash equilibrium problems and Newton methods,, Math. Program., 117 (2009), 163.
doi: 10.1007/s10107-007-0160-2. |
[10] |
M. Fukushima, Restricted generalized Nash equilibria and controlled penalty algorithm,, Comput. Manag. Sci., 8 (2011), 201.
doi: 10.1007/s10287-009-0097-4. |
[11] |
G. Gürkan and J. S. Pang, Approximations of Nash equilibria,, Math. Program., 117 (2009), 223.
doi: 10.1007/s10107-007-0156-y. |
[12] |
P. T. Harker, Generalized Nash games and quasi-variational inequalities,, European J. Oper. Res., 54 (1991), 81.
doi: 10.1016/0377-2217(91)90325-P. |
[13] |
A. V. Heusinger and C. Kanzow, Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions,, Comput. Optim. Appl., 43 (2009), 353.
doi: 10.1007/s10589-007-9145-6. |
[14] |
A. Kesselman, S. Leonardi and V. Bonifaci, Game-theoretic analysis of internet switching with selfish users,, Theoret. Comput. Sci., 452 (2012), 107.
doi: 10.1016/j.tcs.2012.05.029. |
[15] |
J. B. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications,, Environ. Model. Assess., 5 (2000), 63. Google Scholar |
[16] |
T. D. Luca, F. Facchinei and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems,, Math. Program., 75 (1996), 407.
doi: 10.1007/BF02592192. |
[17] |
R. Mifflin, Semismooth and semiconvex functions in constrained optimization,, SIAM J. Control. Optim., 15 (1977), 959.
doi: 10.1137/0315061. |
[18] |
J. S. Pang, G. Scutari, F. Facchinei and C. Wang, Distributed power allocation with rate constraints in Gaussian parallel interference channels,, IEEE Trans. Inform. Theory, 54 (2008), 3471.
doi: 10.1109/TIT.2008.926399. |
[19] |
J. S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games,, Comput. Manag. Sci., 2 (2005), 21.
doi: 10.1007/s10287-004-0010-0. |
[20] |
B. Panicucci, M. Pappalardo and M. Passacantando, On finite-dimensional generalized variational inequalities,, J. Ind. Manag. Optim., 2 (2006), 43.
doi: 10.3934/jimo.2006.2.43. |
[21] |
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations,, Math. Oper. Res., 18 (1993), 227.
doi: 10.1287/moor.18.1.227. |
[22] |
L. Qi and J. Sun, A nonsmooth version of Newton's method,, Math. Program, 58 (1993), 353.
doi: 10.1007/BF01581275. |
[23] |
S. M. Robinson, Shadow prices for measures of effectiveness, I: Linear model,, Oper. Res., 41 (1993), 518.
doi: 10.1287/opre.41.3.518. |
[24] |
S. M. Robinson, Shadow prices for measures of effectiveness, II: General model,, Oper. Res., 41 (1993), 536.
doi: 10.1287/opre.41.3.536. |
[25] |
R. T. Rockafellar and R. J. Wets, Variational Analysis,, Springer-Verlag, (1998).
doi: 10.1007/978-3-642-02431-3. |
[26] |
S. Uryasev and R. Y. Rubinstein, On relaxation algorithms in computation of noncooperative equilibria,, IEEE Trans. Automat. Control., 39 (1994), 1263.
doi: 10.1109/9.293193. |
[27] |
J. Y. Wei and Y. Smeers, Spatial oligopolistic electricity models with cournot generators and regulated transmission prices,, Oper. Res., 47 (1999), 102. Google Scholar |
show all references
References:
[1] |
M. Breton, G. Zaccour and M. Zahaf, A game-theoretic formulation of joint implementation of environmental projects,, European J. Oper. Res., 168 (2006), 221.
doi: 10.1016/j.ejor.2004.04.026. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis,, John Wiley, (1983).
|
[3] |
J. Contreras, M. Klusch and J. B. Krawczyk, Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets,, IEEE. T. Power. Syst., 19 (2004), 195.
doi: 10.1109/TPWRS.2003.820692. |
[4] |
G. Debreu, A social equilibrium existence theorem,, Proc. Natl. Acad. Sci. U. S. A., 38 (1952), 886.
doi: 10.1073/pnas.38.10.886. |
[5] |
F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, I, (2003).
|
[6] |
F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, Vol II, (2003).
|
[7] |
F. Facchinei, A. Fischer and V. Piccialli, On generalized Nash games and variational inequalities,, Oper. Res. Lett., 35 (2007), 159.
doi: 10.1016/j.orl.2006.03.004. |
[8] |
F. Facchinei, A. Fischer and C. Kanzow, Regularity properties of a semismooth reformulation of variational inequalities,, SIAM J. Optim., 8 (1998), 850.
doi: 10.1137/S1052623496298194. |
[9] |
F. Facchinei, A. Fischer and V. Piccialli, Generalized Nash equilibrium problems and Newton methods,, Math. Program., 117 (2009), 163.
doi: 10.1007/s10107-007-0160-2. |
[10] |
M. Fukushima, Restricted generalized Nash equilibria and controlled penalty algorithm,, Comput. Manag. Sci., 8 (2011), 201.
doi: 10.1007/s10287-009-0097-4. |
[11] |
G. Gürkan and J. S. Pang, Approximations of Nash equilibria,, Math. Program., 117 (2009), 223.
doi: 10.1007/s10107-007-0156-y. |
[12] |
P. T. Harker, Generalized Nash games and quasi-variational inequalities,, European J. Oper. Res., 54 (1991), 81.
doi: 10.1016/0377-2217(91)90325-P. |
[13] |
A. V. Heusinger and C. Kanzow, Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions,, Comput. Optim. Appl., 43 (2009), 353.
doi: 10.1007/s10589-007-9145-6. |
[14] |
A. Kesselman, S. Leonardi and V. Bonifaci, Game-theoretic analysis of internet switching with selfish users,, Theoret. Comput. Sci., 452 (2012), 107.
doi: 10.1016/j.tcs.2012.05.029. |
[15] |
J. B. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications,, Environ. Model. Assess., 5 (2000), 63. Google Scholar |
[16] |
T. D. Luca, F. Facchinei and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems,, Math. Program., 75 (1996), 407.
doi: 10.1007/BF02592192. |
[17] |
R. Mifflin, Semismooth and semiconvex functions in constrained optimization,, SIAM J. Control. Optim., 15 (1977), 959.
doi: 10.1137/0315061. |
[18] |
J. S. Pang, G. Scutari, F. Facchinei and C. Wang, Distributed power allocation with rate constraints in Gaussian parallel interference channels,, IEEE Trans. Inform. Theory, 54 (2008), 3471.
doi: 10.1109/TIT.2008.926399. |
[19] |
J. S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games,, Comput. Manag. Sci., 2 (2005), 21.
doi: 10.1007/s10287-004-0010-0. |
[20] |
B. Panicucci, M. Pappalardo and M. Passacantando, On finite-dimensional generalized variational inequalities,, J. Ind. Manag. Optim., 2 (2006), 43.
doi: 10.3934/jimo.2006.2.43. |
[21] |
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations,, Math. Oper. Res., 18 (1993), 227.
doi: 10.1287/moor.18.1.227. |
[22] |
L. Qi and J. Sun, A nonsmooth version of Newton's method,, Math. Program, 58 (1993), 353.
doi: 10.1007/BF01581275. |
[23] |
S. M. Robinson, Shadow prices for measures of effectiveness, I: Linear model,, Oper. Res., 41 (1993), 518.
doi: 10.1287/opre.41.3.518. |
[24] |
S. M. Robinson, Shadow prices for measures of effectiveness, II: General model,, Oper. Res., 41 (1993), 536.
doi: 10.1287/opre.41.3.536. |
[25] |
R. T. Rockafellar and R. J. Wets, Variational Analysis,, Springer-Verlag, (1998).
doi: 10.1007/978-3-642-02431-3. |
[26] |
S. Uryasev and R. Y. Rubinstein, On relaxation algorithms in computation of noncooperative equilibria,, IEEE Trans. Automat. Control., 39 (1994), 1263.
doi: 10.1109/9.293193. |
[27] |
J. Y. Wei and Y. Smeers, Spatial oligopolistic electricity models with cournot generators and regulated transmission prices,, Oper. Res., 47 (1999), 102. Google Scholar |
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