Một phương pháp điều chỉnh mới cho các bài toán cân bằng trên các đa tạp Hadamard: ứng dụng vào các lý thuyết về ham muốn

Batista, E. E. A., Bento, G. C., & Ferreira, O. P. (2016). Enlargement of monotone vector fields and an inexact proximal point method for variational inequalities in Hadamard manifolds. Journal of Optimization Theory and Applications, 170(3), 916–931. Bento, G. C., & Melo, J. G. (2012). Subgradient method for convex feasibility on Riemannian manifolds. Journal of Optimization Theory and Applications, 152(3), 773–785. Bianchi, M., & Schaible, S. (1996). Generalized monotone bifunctions and equilibrium problems. Journal of Optimization Theory and Applications, 90, 31–43. Blum, E., & Oettli, W. (1994). From optimization and variational inequalities to equilibrium problems. Mathematical Studies, 63, 123–145. Bulavsky, V. A., & Kalashnikov, V. V. (1998). A Newton-like approach to solving an equilibrium problem. Annals of Operations Research, 81, 115–128. Colao, V., López, G., Marino, G., & Martín-Márquez, V. (2012). Equilibrium problems in Hadamard manifolds. Journal of Mathematical Analysis and Applications, 388, 61–77. Cruz Neto, J. X., Ferreira, O. P., & Lucambio Pérez, L. R. (2002). Contributions to the study of monotone vector fields. Acta Mathematica Hungarica, 94(4), 307–320. Cruz Neto, J. X., Ferreira, O. P., Lucambio Pérez, L. R., & Németh, S. Z. (2006). Convex and monotone-transformable mathematical programming problems and a proximal-like point method. Journal of Global Optimization, 35(1), 53–69. Cruz Neto, J. X., Jacinto, F. M. O., Soares, P. A, Jr., & Souza, J. C. O. (2018b). On maximal monotonicity of bifunctions on Hadamard manifolds. Journal of Global Optimization, 72(3), 591–601. Cruz Neto, J. X., Oliveira, P. R., Soares, P. A, Jr., & Soubeyran, A. (2014). Proximal point method on Finslerian manifolds and the effort accuracy trade-off. Journal of Optimization Theory and Applications, 162(3), 873–891. Cruz Neto, J. X., Oliveira, P. R., Soubeyran, A., & Souza, J. C. O. (2018a). A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem. Annals of Operations Research, 1–27. Cruz Neto, J. X., Santos, P. S. M., & Soares, P. A, Jr. (2016). An extragradient method for equilibrium problems on Hadamard manifolds. Optimization Letters, 10, 1327–1336. Cruz Neto, J. X., Santos, P. S. M., & Souza, S. S. (2013). A sufficient descent direction method for quasiconvex optimization over Riemannian manifolds. Pacific Journal of Optimization, 8(4), 803–815. Facchinei, F., & Kanzow, C. (2010). Generalized Nash equilibrium problems. Annals of Operations Research, 175, 177–211. Ferreira, O. P., Lucambio Pérez, L. R., & Németh, S. Z. (2005). Singularities of monotone vector fields and an extragradient-type algorithm. Journal of Global Optimization, 31, 133–151. Ferreira, O. P., & Oliveira, P. R. (2002). Proximal point algorithm on Riemannian manifold. Optimization, 51, 257–270. Haesen, S., Sebekovic, A., & Verstraelen, L. (2003). Relations between intrinsic and extrinsic curvatures. Kragujevac Journal of Mathematics, 25, 139–145. Iusem, A. N., Kassay, G., & Sosa, W. (2009). On certain conditions for the existence of solutions of equilibrium problems. Mathematical Programming Series B, 116, 259–273. Iusem, A. N., & Sosa, W. (2003). New existence results for equilibrium problems. Nonlinear Analysis, 52, 621–635. Iusem, A. N., & Sosa, W. (2010). On the proximal point method for equilibrium problems in Hilbert spaces. Optimization, 59, 1259–1274. Konnov, I. V. (2003). Application of the proximal method to non-monotone equilibrium problems. Journal of Optimization Theory and Applications, 119, 317–333. Kristály, A. (2014). Nash-type equilibria on Riemannian manifolds: A variational approach. Journal de Mathématiques Pures et Appliquées, 101(5), 660–688. Kristály, A., Li, C., López-Acedo, G., et al. (2016). What do ‘Convexities’ imply on Hadamard manifolds? Journal of Optimization Theory and Applications, 170(3), 1068–1074. Ledyaev, Yu S, & Zhu, Q. J. (2007). Nonsmooth analysis on smooth manifolds. Transactions of the American Mathematical Society, 359, 3687–3732. Li, C., Lopéz, G., & Martín-Márquez, V. (2009). Monotone vector fields and the proximal point algorithm on Hadamard manifolds. Journal of the London Mathematical Society, 79(2), 663–683. Li, C., Lopéz, G., Martín-Márquez, V., & Wang, J. H. (2011a). Resolvents of set valued monotone vector fields in Hadamard manifolds. Set-Valued and Variational Analysis, 19(3), 361–383. Li, C., Lopéz, G., Wang, X., & Yao, J. C. (2019). Equilibrium problems on Riemannian manifolds with applications. Journal of Mathematical Analysis and Applications, 473, 866–891. Li, C., Mordukhovich, B. S., Wang, J., & Yao, J. C. (2011b). Weak sharp minima on Riemannian manifolds. SIAM Journal on Optimization, 21(4), 1523–1560. Li, C., & Yao, J. C. (2012). Variational inequalities for set-valued vector fields on Riemannian manifolds: Convexity of the solution set and the proximal point algorithm. SIAM Journal on Control and Optimization, 50(4), 2486–2514. Li, S. L., Li, C., Liou, Y. C., & Yao, J. C. (2009). Existence of solutions for variational inequalities on Riemannian manifolds. Nonlinear Analysis, 71, 5695–5706. Lewin, K. (1935). A dynamic theory of personality. New York: McGraw-Hill. Lewin, K. (1936). Principles of topological psychology. New York: McGraw-Hill. Lewin, K. (1938). The conceptual representation and measurement of psychological forces. Durham: Duke University Press. Lewin, K. (1951). Field theory in social science. New York: Harper. Moudafi, A. (1999). Proximal point algorithm extended for equilibrium problems. Journal of Natural Geometry, 15, 91–100. Németh, S. Z. (2003). Variational inequalities on Hadamard manifolds. Nonlinear Analysis, 52, 1491–1498. Ng, L. (1995). Classical and modern formulations of curvature. Mathematics, 230a. Pany, G., Mohapatra, R. N., & Pani, S. (2018). Solution of a class of equilibrium problems and variational inequalities in FC spaces. Annals of Operations Research, 269, 565–582. Quiroz, E. A. P. (2013). An extension of the proximal point algorithm with Bregman distances on Hadamard manifolds. Journal of Global Optimization, 56, 43–59. Rapcsák, T. (1997). Smooth nonlinear optimization in \({\mathbb{R}}^n\). In Nonconvex optimization and its applications (Vol. 19). Dordrecht: Kluwer Academic Publishers. Sakai, T. (1996). Riemannian geometry, Transl. Math. Monogr. (Vol. 149). Providence: Amer. Math. Soc. Soubeyran, A. (2009). Variational rationality, a theory of individual stability and change: worthwhile and ambidextry behaviors. Preprint. GREQAM, Aix Marseille University. Soubeyran, A. (2010). Variational rationality and the “unsatisfied man”: Routines and the course pursuit between aspirations, capabilities and beliefs. Preprint. GREQAM, Aix Marseille University. Soubeyran, A. (2015). Variational rationality. Traps, or desires, as ends of stay and change worthwhile transitions, GREQAM, AMSE, Aix-Marseille University. Soubeyran, A. (2016). Variational rationality. A theory of worthwhile stay and change approach-avoidance transitions ending in traps, Preprint, GREQAM-AMSE, Aix Marseille University. Soubeyran, A. (2019). Variational rationality. 1. An adaptive theory of the unsatisfied man, Preprint. AMSE. Aix-Marseille University. Soubeyran, A. (2019). Variational rationality. 2. A general theory of goals and intentions as satisficing worthwhile moves, Preprint. AMSE, Aix-Marseille University. Tang, G., Zhou, L., & Huang, N. (2013). The proximal point algorithm for pseudomonotone variational inequalities on Hadamard manifolds. Optimization Letters, 7, 779–790. Udriste, C. (1994). Convex functions and optimization methods on Riemannian manifolds, mathematics and its applications (Vol. 297). Dordrecht: Kluwer Academic Publishers. Yang, W. H., Zhang, L.-H., & Song, R. (2013). Optimality conditions for the nonlinear programming problems on Riemannian manifolds. Pacific Journal of Optimization, 10(2), 415–434.