An algorithm for minimizing a strongly convex function on the equilibrium set of price equilibrium models
Tóm tắt
Từ khóa
#Equilibrium model #variational inequality #bilevel optimization algorithm #regularizationTài liệu tham khảo
Bauschke, H. H., Combettes, P. L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011).
Deutsch, F., Yamada, I. Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansivemappings, Numer. Funct. Anal, Optim. 19, 33-56 (1998).
Dinh, B. V., Hung, P. G., Muu, L. D. Bilevel optimization as a regularization approach to pseudomonotone equilibrium problems, Numer. Funct. Anal. Optim. 35, 539-563 (2014)
Facchinei, F., Pang, J. S. Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol. 1,2, Springer-Verlag, Berlin (2003).
Hai, N. N., Muu, L. D., Dinh, B. V. An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand, Math. Methods Oper. Res. 98, 299-324 (2023).
Golshtein, E. G., Tretyakov, N. V. Modifed Lagrangians and Monotone Maps in Optimization, Wiley, New York, NY (1996).
Konnov, I. V. Combined Relaxation Methods for Variational Inequalities, Springer-Verlag, Berlin (2000).
Konnov, I. V. Economics Models and Variational Inequalities, Elsevier (2007).
Muu, L. D., Quoc, T. D. Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model, J. Optim. Theory Appl. 142, 185-204 (2009).
Rockafellar, R. T. Monotone operator and the proximal point algorithm, SIAM J. Control and Optim. 14, 877-898 (1976).
Tuy, H. Convex Analysis and Global Optimization, Springer, Berlin (2016).
Walras, L. El´ements d’´Economie Politique Pure (1874), L. Corbaz, Lausanne; English translation.: Elements of Pure Economics, Allen and Unwin, London (1954).
Xu, H. K. Iterative algorithms for nonlinear operators. J. London Math. Soc. 66 : 240-256 (2002).
Yamada, I., Ogura, N. Hybrid steepest descent method for variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings, Numer. Funct. Anal. Optim. 25 , 178-189 (2005).
Zhu, D., Marcotte, P. A new class of generalized monotonicity, J. Optim. Theory Appl. 67, 457-471 (1995).
