Tính nửa liên tục trên của ánh xạ nghiệm bài toán cân bằng mạnh theo nón Lorentz
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Anh, L.Q., Duy T.Q., Kruger, A.Y., Thao, N.H., 2014. Well-posedness for lexicographic vector equilibrium problems. In: Vladimir, D., Panos, M.P., Mikhail, B. (Eds). Constructive Nonsmooth Analysis and Related Topics. Springer Optimization and Its Applications. Springer-Verlag, Berlin. 87: 157–172.
Anh, P.N., Hai, T.N., Tuan, P.M., 2015. On ergodic algorithms for equilibrium problems. Journal of Global Optimization. 64: 179 –195.
Anh, L.Q., Khanh, P.Q., 2007. On the stability of the solution sets of general multivalued vector quasiequilibrium problems. Journal of Optimization Theory and Applications. 135: 271–284.
Anh, L.Q., Khanh, P.Q., 2010. Continuity of solution maps of parametric quasiequilibrium problems. Journal of Global Optimization. 46: 247–259.
Anh, L.Q., Khanh, P.Q., Van, D.T.M., 2012. Well-posedness under relaxed semicontinuity for bilevel equilibrium and optimization problems with equilibrium constraints. Journal of Optimization Theory and Applications.153: 42–59.
Anh, L.Q., Khanh, P.Q., Van, D.T.M., Yao, J.C., 2009. Well-posedness for vector quasiequilibria, Taiwanese Journal of Mathematics. 13: 713–737.
Ansari, Q.H., Yang, X.Q., Yao, J.C., 2001. Existence and duality of implicit vector variational problems. Numerical Functional Analysis and Optimization. 22: 815–829.
Aubin, J.P., Frankowska, H., 1990. Set-Valued Analysis. Birkhäuser Boston Inc., Boston. 33–48.
Bianchi, M., Pini, R., 2003. A note on stability for parametric equilibrium problems. Operations Research Letters. 31: 445–450.
Bigi, G., Castellani, M., Pappalardo, M., Passacantando, M., 2013. Existence and solution methods for equilibria. European Journal of Operational Research. 227: 1–11.
Blum, E., Oettli, W., 1994. From optimization and variational inequalities to equilibrium problems. The Mathematics Student. 63: 123–145.
Chi, X., Liu, S., 2009. A one-step smoothing Newton method for second-order cone programming. Journal of Computational and Applied Mathematics. 223: 114–123.
Dong, L., Tang, J., Zhou, J., 2012. A smoothing Newton algorithm for solving the monotone second-order cone complementarity problems. Journal of Applied Mathematics and Computing. 40: 45–61.
Fang, L., He, G., Hu, Y., 2009. A new smoothing Newton-type method for second-order cone programming problems. Applied Mathematics and Computation. 215: 1020–1029.
Fu, J.Y., Wan, A.H., 2002. Generalized vector equilibrium problems with set-valued mappings. Mathematical Methods of Operations Research. 56: 259–268.
Iusem, A.N., Sosa, W., 2010. On the proximal point method for equilibrium problems in Hilbert spaces. Optimization 59: 1259–1274.
Kimura, K., Liou, Y.C., Wu, S.Y., Yao, J.C., 2008. Well-posedness for parametric vector equilibrium problems with applications. Journal of Industrial and Management Optimization. 4: 313–327.
Muu, L.D., Quy, N.V., 2015. On existence and solution methods for strongly pseudomonotone equilibrium problems. Vietnam Journal of Mathematics. 43: 229–238.
Pedro G., Alberto S., 2012. Equilibrium problems involving the Lorentz cone. Journal of Global Optimization. 58: 321–340.
Quoc, T.D., Anh, P.N., Muu, L.D., 2012. Dual extragradient algorithms extended to equilibrium problems. Journal of Global Optimization. 52: 139–159.
Wu, J., Chen, J. S., 2012. A proximal point algorithm for the monotone second-order cone complementarity problem. Computational Optimization and Applications. 51:1037–1063.