[37] D. Kim and J. A. Fessler. Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions. Journal of Optimization Theory and Applications, 188(1): 192-219, 2021.
[38] J. Kim and I. Yang. Unifying Nesterov's accelerated gradient methods for convex and strongly convex objective functions. International Conference on Machine Learning, 202, 2023.
[39] U. Kohlenbach. On quantitative versions of theorems due to F. E. Browder and R. Wittmann. Advances in Mathematics, 226(3):2764-2795, 2011.
[40] M. A. Krasnosel'skii. Two remarks on the method of successive approximations. *Uspekhi Matematicheskikh Nauk*, 10(1):123–127, 1955.
[41] J. Lee and E. K. Ryu. Accelerating value iteration with anchoring. Neural Information Processing Systems, 2023.
[42] S. Lee and D. Kim. Fast extra gradient methods for smooth structured nonconvex-nonconcave minimax problems. Neural Information Processing Systems, 2021.
[43] L. Leustean. Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings. Journal of Universal Computer Science, 13(11):1680-1691, 2007.
[44] J. Liang, J. Fadili, and G. Peyre. Convergence rates with inexact non-expansive operators. Mathematical Programming, 159(1):403-434, 2016.
[45] F. Lieder. On the convergence rate of the Halpern-iteration. Optimization Letters, 15(2): 405-418, 2021.
[46] T. Lin and M. I. Jordan. Monotone Inclusions, Acceleration, and Closed-Loop Control. Mathematics of Operations Research, 2023.
[47] W. R. Mann. Mean value methods in iteration. Proceedings of the American Mathematical Society, 4(3):506-510, 1953.
[48] B. Martinet. Régularisation d'inéquations variationnelles par approximations successives. Revue Française d'Informatique et de Recherche Opérationnelle, Série Rouge, 4(3):154-158, 1970.
[49] B. Martinet. Algorithms Pour La Résolution de Problèmes d'optimisation et de Minimax. PhD thesis, Université Scientifique et Médicale de Grenoble, 1972.
[50] S.-Y. Matsushita. On the convergence rate of the Krasnosel'skii-Mann iteration. Bulletin of the Australian Mathematical Society, 96(1):162-170, 2017.
[51] Y. Nesterov. A method of solving a convex programming problem with convergence rate  $O(1 / k^2)$ . Doklady Akademii Nauk SSSR, 269(3):543-547, 1983.
[52] Y. Nesterov. Introductory Lectures on Convex Optimization: A Basic Course. Springer, 2004.
[53] C. Park, J. Park, and E. K. Ryu. Factor- $\sqrt{2}$  acceleration of accelerated gradient methods. Applied Mathematics and Optimization, 2022.
[54] J. Park and E. K. Ryu. Exact optimal accelerated complexity for fixed-point iterations. International Conference on Machine Learning, 2022.
[55] J. Park and E. K. Ryu. Accelerated infeasibility detection of constrained optimization and fixed-point iterations. International Conference on Machine Learning, 2023.
[56] L. D. Popov. A modification of the Arrow-Hurwicz method for search of saddle points. Mathematical Notes of the Academy of Sciences of the USSR, 28(5):845-848, 1980.
[57] A. Rakhlin and K. Sridharan. Online learning with predictable sequences. Conference on Learning Theory, 2013.
[58] E. K. Ryu and W. Yin. Large-Scale Convex Optimization via Monotone Operators. Cambridge University Press, 2022.