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Preface
1. | University of Würzburg, Institute of Mathematics, Am Hubland, 97074 Würzburg |
2. | School of Mathematical Sciences, South China Normal University, Guangzhou, 510631 |
3. | Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501 |
For more information please click the “Full Text” above.
References:
[1] |
H. Mine, K. Ohno and M. Fukushima, A "conjugate" interior penalty method for certain convex programs, SIAM Journal on Control and Optimization, 15 (1977), 747-755.
doi: 10.1137/0315047. |
[2] |
H. Mine and M. Fukushima, A minimization method for the sum of a convex function and a continuously differentiable function, Journal of Optimization Theory and Applications, 33 (1981), 9-23.
doi: 10.1007/BF00935173. |
[3] |
M. Fukushima and H. Mine, A generalized proximal point algorithm for certain nonconvex minimization problems, International Journal of Systems Science, 12 (1981), 989-1000.
doi: 10.1080/00207728108963798. |
[4] |
M. Fukushima, An outer approximation algorithm for solving general convex programs, Operations Research, 31 (1983), 101-113.
doi: 10.1287/opre.31.1.101. |
[5] |
M. Fukushima, A fixed point approach to certain convex programs with applications in stochastic programming, Mathematics of Operations Research, 8 (1983), 517-524.
doi: 10.1287/moor.8.4.517. |
[6] |
M. Fukushima, On the convergence of a class of outer approximation algorithms for convex programs, Journal of Computational and Applied Mathematics, 10 (1984), 147-156.
doi: 10.1016/0377-0427(84)90051-7. |
[7] |
M. Fukushima, A modified Frank-Wolfe algorithm for solving the traffic assignment problem, Transportation Research, 18B (1984), 169-177.
doi: 10.1016/0191-2615(84)90029-8. |
[8] |
M. Fukushima, On the dual approach to the traffic assignment problem, Transportation Research, 18B (1984), 235-245.
doi: 10.1016/0191-2615(84)90034-1. |
[9] |
M. Fukushima, A nonsmooth optimization approach to nonlinear multicommodity network flow problems, Journal of the Operations Research Society of Japan, 27 (1984), 151-176. |
[10] |
M. Fukushima, A descent algorithm for nonsmooth convex optimization, Mathematical Programming, 30 (1984), 163-175.
doi: 10.1007/BF02591883. |
[11] |
M. Fukushima, A relaxed projection method for variational inequalities, Mathematical Programming, 35 (1986), 58-70.
doi: 10.1007/BF01589441. |
[12] |
M. Fukushima, A successive quadratic programming algorithm with global and superlinear convergence properties, Mathematical Programming, 35 (1986), 253-264.
doi: 10.1007/BF01580879. |
[13] |
E. Yamakawa, M. Fukushima and T. Ibaraki, An efficient trust region algorithm for minimizing nondifferentiable composite functions, SIAM Journal on Scientific and Statistical Computing, 10 (1989), 562-580.
doi: 10.1137/0910036. |
[14] |
M. Fukushima, A conjugate gradient algorithm for sparse linear inequalities, Journal of Computational and Applied Mathematics, 30 (1990), 329-339.
doi: 10.1016/0377-0427(90)90283-6. |
[15] |
M. Fukushima, A successive quadratic programming method for a class of constrained nonsmooth optimization problems, Mathematical Programming, 49 (1991), 231-251.
doi: 10.1007/BF01588789. |
[16] |
M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[17] |
M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93-111.
doi: 10.1007/BF00247655. |
[18] |
K. Taji, M. Fukushima and T. Ibaraki, A globally convergent Newton method for solving strongly monotone variational inequalities, Mathematical Programming, 58 (1993), 369-383.
doi: 10.1007/BF01581276. |
[19] |
N. Yamashita and M. Fukushima, On stationary points of the implicit Lagrangian for nonlinear complementarity problems, Journal of Optimization Theory and Applications, 84 (1995), 653-663.
doi: 10.1007/BF02191990. |
[20] |
M. Fukushima, The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem, Mathematical Programming, 72 (1996), 1-15.
doi: 10.1007/BF02592328. |
[21] |
P. Tseng, N. Yamashita and M. Fukushima, Equivalence of complementarity problems to differentiable minimization: A unified approach, SIAM Journal on Optimization, 6 (1996), 446-460.
doi: 10.1137/0806024. |
[22] |
M. Fukushima, Merit functions for variational inequality and complementarity problems, in "Nonlinear Optimization and Applications " (eds. G. Di Pillo and F. Giannessi), Plenum Press, (1996), 155-170. |
[23] |
K. Taji and M. Fukushima, A new merit function and a successive quadratic programming algorithm for variational inequality problems, SIAM Journal on Optimization, 6 (1996), 704-713.
doi: 10.1137/S1052623494271199. |
[24] |
M. Fukushima and L. Qi, A globally and superlinearly convergent algorithm for nonsmooth convex minimization, SIAM Journal on Optimization, 6 (1996), 1106-1120.
doi: 10.1137/S1052623494278839. |
[25] |
N. Yamashita, K. Taji and M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, Journal of Optimization Theory and Applications, 92 (1997), 439-456.
doi: 10.1023/A:1022660704427. |
[26] |
H. Jiang, M. Fukushima, L. Qi and D. Sun, A trust region method for solving generalized complementarity problems, SIAM Journal on Optimization, 8 (1998), 140-157.
doi: 10.1137/S1052623495296541. |
[27] |
M. Fukushima, Z. Q. Luo and J. S. Pang, A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints, Computational Optimization and Applications, 10 (1998) 5-34.
doi: 10.1023/A:1018359900133. |
[28] |
M. Fukushima, Parallel variable transformation in unconstrained optimization, SIAM Journal on Optimization, 8 (1998), 658-672.
doi: 10.1137/S1052623496309879. |
[29] |
M. Fukushima and J. S. Pang, Some feasibility issues in mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 8 (1998), 673-681.
doi: 10.1137/S105262349731577X. |
[30] |
C. Kanzow and M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Mathematical Programming, 83 (1998), 55-87.
doi: 10.1007/BF02680550. |
[31] |
J.-S. Pang and M. Fukushima, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints, Computational Optimization and Applications, 13 (1999), 111-136.
doi: 10.1023/A:1008656806889. |
[32] |
X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming, 85 (1999), 313-334.
doi: 10.1007/s101070050059. |
[33] |
M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints, in "Ill-posed Variational Problems and Regularization Techniques" (eds. M. Thera and R. Tichatschke), Lecture Notes in Economics and Mathematical Systems, 477 (1999), Springer-Verlag, Berlin/Heidelberg, 99-110. |
[34] |
N. Yamashita and M. Fukushima, The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem, SIAM Journal on Optimization, 11 (2001), 364-379.
doi: 10.1137/S105262349935949X. |
[35] |
D. Li and M. Fukushima, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems, SIAM Journal on Optimization, 11 (2001), 1054-1064.
doi: 10.1137/S1052623499354242. |
[36] |
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. |
[37] |
M. Fukushima and P. Tseng, An implementable active-set algorithm for computing a B-stationary point of the mathematical program with linear complementarity constraints, SIAM Journal on Optimization, 12 (2002), 724-739. [Erratum,
doi: 10.1137/S1052623499363232. |
[38] |
M. Fukushima, Z.-Q. Luo and P. Tseng, A sequential quadratically constrained quadratic programming method for differentiable convex minimization, SIAM Journal on Optimization, 13 (2003), 1098-1119.
doi: 10.1137/S1052623401398120. |
[39] |
J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games, Computational Management Science, 2 (2005), 21-56. [Erratum,
doi: 10.1007/s10287-004-0010-0. |
[40] |
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. |
[41] |
X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Mathematics of Operations Research, 30 (2005), 1022-1038.
doi: 10.1287/moor.1050.0160. |
[42] |
P. Zhong and M. Fukushima, Second order cone programming formulations for robust multi-class classification, Neural Computation, 19 (2007), 258-282.
doi: 10.1162/neco.2007.19.1.258. |
[43] |
M. Fukushima, A class of gap functions for quasi-variational inequality problems, Journal of Industrial and Management Optimization, 3 (2007), 165-171. |
[44] |
M. A. Majig, A. R. Hedar and M. Fukushima, Hybrid evolutionary algorithm for solving general variational inequality problems, Journal of Global Optimization, 38 (2007), 637-651.
doi: 10.1007/s10898-006-9102-4. |
[45] |
H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ matrix linear complementarity problems, SIAM Journal on Optimization, 18 (2007), 482-506.
doi: 10.1137/050630805. |
[46] |
G. H. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming, 116 (2009), 343-368.
doi: 10.1007/s10107-007-0119-3. |
[47] |
X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Mathematical Programming, 117 (2009), 51-80.
doi: 10.1007/s10107-007-0163-z. |
[48] |
C. Kanzow, I. Ferenczi and M. Fukushima, On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity, SIAM Journal on Optimization, 20 (2009), 297-320.
doi: 10.1137/060657662. |
[49] |
S. S. Zhu and M. Fukushima, Worst-case conditional Value-at-Risk with application to robust portfolio management, Operations Research, 57 (2009), 1155-1168.
doi: 10.1287/opre.1080.0684. |
[50] |
G. H. Lin and M. Fukushima, Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey, Pacific Journal of Optimization, 6 (2010), 455-482. |
show all references
References:
[1] |
H. Mine, K. Ohno and M. Fukushima, A "conjugate" interior penalty method for certain convex programs, SIAM Journal on Control and Optimization, 15 (1977), 747-755.
doi: 10.1137/0315047. |
[2] |
H. Mine and M. Fukushima, A minimization method for the sum of a convex function and a continuously differentiable function, Journal of Optimization Theory and Applications, 33 (1981), 9-23.
doi: 10.1007/BF00935173. |
[3] |
M. Fukushima and H. Mine, A generalized proximal point algorithm for certain nonconvex minimization problems, International Journal of Systems Science, 12 (1981), 989-1000.
doi: 10.1080/00207728108963798. |
[4] |
M. Fukushima, An outer approximation algorithm for solving general convex programs, Operations Research, 31 (1983), 101-113.
doi: 10.1287/opre.31.1.101. |
[5] |
M. Fukushima, A fixed point approach to certain convex programs with applications in stochastic programming, Mathematics of Operations Research, 8 (1983), 517-524.
doi: 10.1287/moor.8.4.517. |
[6] |
M. Fukushima, On the convergence of a class of outer approximation algorithms for convex programs, Journal of Computational and Applied Mathematics, 10 (1984), 147-156.
doi: 10.1016/0377-0427(84)90051-7. |
[7] |
M. Fukushima, A modified Frank-Wolfe algorithm for solving the traffic assignment problem, Transportation Research, 18B (1984), 169-177.
doi: 10.1016/0191-2615(84)90029-8. |
[8] |
M. Fukushima, On the dual approach to the traffic assignment problem, Transportation Research, 18B (1984), 235-245.
doi: 10.1016/0191-2615(84)90034-1. |
[9] |
M. Fukushima, A nonsmooth optimization approach to nonlinear multicommodity network flow problems, Journal of the Operations Research Society of Japan, 27 (1984), 151-176. |
[10] |
M. Fukushima, A descent algorithm for nonsmooth convex optimization, Mathematical Programming, 30 (1984), 163-175.
doi: 10.1007/BF02591883. |
[11] |
M. Fukushima, A relaxed projection method for variational inequalities, Mathematical Programming, 35 (1986), 58-70.
doi: 10.1007/BF01589441. |
[12] |
M. Fukushima, A successive quadratic programming algorithm with global and superlinear convergence properties, Mathematical Programming, 35 (1986), 253-264.
doi: 10.1007/BF01580879. |
[13] |
E. Yamakawa, M. Fukushima and T. Ibaraki, An efficient trust region algorithm for minimizing nondifferentiable composite functions, SIAM Journal on Scientific and Statistical Computing, 10 (1989), 562-580.
doi: 10.1137/0910036. |
[14] |
M. Fukushima, A conjugate gradient algorithm for sparse linear inequalities, Journal of Computational and Applied Mathematics, 30 (1990), 329-339.
doi: 10.1016/0377-0427(90)90283-6. |
[15] |
M. Fukushima, A successive quadratic programming method for a class of constrained nonsmooth optimization problems, Mathematical Programming, 49 (1991), 231-251.
doi: 10.1007/BF01588789. |
[16] |
M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[17] |
M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93-111.
doi: 10.1007/BF00247655. |
[18] |
K. Taji, M. Fukushima and T. Ibaraki, A globally convergent Newton method for solving strongly monotone variational inequalities, Mathematical Programming, 58 (1993), 369-383.
doi: 10.1007/BF01581276. |
[19] |
N. Yamashita and M. Fukushima, On stationary points of the implicit Lagrangian for nonlinear complementarity problems, Journal of Optimization Theory and Applications, 84 (1995), 653-663.
doi: 10.1007/BF02191990. |
[20] |
M. Fukushima, The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem, Mathematical Programming, 72 (1996), 1-15.
doi: 10.1007/BF02592328. |
[21] |
P. Tseng, N. Yamashita and M. Fukushima, Equivalence of complementarity problems to differentiable minimization: A unified approach, SIAM Journal on Optimization, 6 (1996), 446-460.
doi: 10.1137/0806024. |
[22] |
M. Fukushima, Merit functions for variational inequality and complementarity problems, in "Nonlinear Optimization and Applications " (eds. G. Di Pillo and F. Giannessi), Plenum Press, (1996), 155-170. |
[23] |
K. Taji and M. Fukushima, A new merit function and a successive quadratic programming algorithm for variational inequality problems, SIAM Journal on Optimization, 6 (1996), 704-713.
doi: 10.1137/S1052623494271199. |
[24] |
M. Fukushima and L. Qi, A globally and superlinearly convergent algorithm for nonsmooth convex minimization, SIAM Journal on Optimization, 6 (1996), 1106-1120.
doi: 10.1137/S1052623494278839. |
[25] |
N. Yamashita, K. Taji and M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, Journal of Optimization Theory and Applications, 92 (1997), 439-456.
doi: 10.1023/A:1022660704427. |
[26] |
H. Jiang, M. Fukushima, L. Qi and D. Sun, A trust region method for solving generalized complementarity problems, SIAM Journal on Optimization, 8 (1998), 140-157.
doi: 10.1137/S1052623495296541. |
[27] |
M. Fukushima, Z. Q. Luo and J. S. Pang, A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints, Computational Optimization and Applications, 10 (1998) 5-34.
doi: 10.1023/A:1018359900133. |
[28] |
M. Fukushima, Parallel variable transformation in unconstrained optimization, SIAM Journal on Optimization, 8 (1998), 658-672.
doi: 10.1137/S1052623496309879. |
[29] |
M. Fukushima and J. S. Pang, Some feasibility issues in mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 8 (1998), 673-681.
doi: 10.1137/S105262349731577X. |
[30] |
C. Kanzow and M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Mathematical Programming, 83 (1998), 55-87.
doi: 10.1007/BF02680550. |
[31] |
J.-S. Pang and M. Fukushima, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints, Computational Optimization and Applications, 13 (1999), 111-136.
doi: 10.1023/A:1008656806889. |
[32] |
X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming, 85 (1999), 313-334.
doi: 10.1007/s101070050059. |
[33] |
M. Fukushima and J. S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints, in "Ill-posed Variational Problems and Regularization Techniques" (eds. M. Thera and R. Tichatschke), Lecture Notes in Economics and Mathematical Systems, 477 (1999), Springer-Verlag, Berlin/Heidelberg, 99-110. |
[34] |
N. Yamashita and M. Fukushima, The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem, SIAM Journal on Optimization, 11 (2001), 364-379.
doi: 10.1137/S105262349935949X. |
[35] |
D. Li and M. Fukushima, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems, SIAM Journal on Optimization, 11 (2001), 1054-1064.
doi: 10.1137/S1052623499354242. |
[36] |
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. |
[37] |
M. Fukushima and P. Tseng, An implementable active-set algorithm for computing a B-stationary point of the mathematical program with linear complementarity constraints, SIAM Journal on Optimization, 12 (2002), 724-739. [Erratum,
doi: 10.1137/S1052623499363232. |
[38] |
M. Fukushima, Z.-Q. Luo and P. Tseng, A sequential quadratically constrained quadratic programming method for differentiable convex minimization, SIAM Journal on Optimization, 13 (2003), 1098-1119.
doi: 10.1137/S1052623401398120. |
[39] |
J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games, Computational Management Science, 2 (2005), 21-56. [Erratum,
doi: 10.1007/s10287-004-0010-0. |
[40] |
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. |
[41] |
X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Mathematics of Operations Research, 30 (2005), 1022-1038.
doi: 10.1287/moor.1050.0160. |
[42] |
P. Zhong and M. Fukushima, Second order cone programming formulations for robust multi-class classification, Neural Computation, 19 (2007), 258-282.
doi: 10.1162/neco.2007.19.1.258. |
[43] |
M. Fukushima, A class of gap functions for quasi-variational inequality problems, Journal of Industrial and Management Optimization, 3 (2007), 165-171. |
[44] |
M. A. Majig, A. R. Hedar and M. Fukushima, Hybrid evolutionary algorithm for solving general variational inequality problems, Journal of Global Optimization, 38 (2007), 637-651.
doi: 10.1007/s10898-006-9102-4. |
[45] |
H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ matrix linear complementarity problems, SIAM Journal on Optimization, 18 (2007), 482-506.
doi: 10.1137/050630805. |
[46] |
G. H. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming, 116 (2009), 343-368.
doi: 10.1007/s10107-007-0119-3. |
[47] |
X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Mathematical Programming, 117 (2009), 51-80.
doi: 10.1007/s10107-007-0163-z. |
[48] |
C. Kanzow, I. Ferenczi and M. Fukushima, On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity, SIAM Journal on Optimization, 20 (2009), 297-320.
doi: 10.1137/060657662. |
[49] |
S. S. Zhu and M. Fukushima, Worst-case conditional Value-at-Risk with application to robust portfolio management, Operations Research, 57 (2009), 1155-1168.
doi: 10.1287/opre.1080.0684. |
[50] |
G. H. Lin and M. Fukushima, Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey, Pacific Journal of Optimization, 6 (2010), 455-482. |
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