Cabot, A., Engler, H., and Gadat, S. (2009). On the long time behavior of second order differential equations with asymptotically small dissipation. Trans. Amer. Math. Soc., 361(11):5983-6017.
Celledoni, E., Eidnes, S., Owren, B., and Ringholm, T. (2018). Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows. SIAM J. Sci. Comput., 40(6):A3789-A3806.
Chen, L. and Luo, H. (2021). A unified convergence analysis of first order convex optimization methods via strong lyapunov functions. arXiv preprint, arXiv:2108.00132.
De Sa, C. M., Kale, S., Lee, J. D., Sekhari, A., and Sridharan, K. (2022). From gradient flow on population loss to learning with stochastic gradient descent. In Advances in Neural Information Processing Systems, volume 35, pages 30963-30976.
Defazio, A. (2019). On the curved geometry of accelerated optimization. In Advances in Neural Information Processing Systems, volume 32.
Diakonikolas, J. and Orecchia, L. (2019). The approximate duality gap technique: a unified theory of first-order methods. SIAM J. Optim., 29(1):660-689.
Drori, Y. and Taylor, A. (2022). On the oracle complexity of smooth strongly convex minimization. J. Complexity, 68:101590.
Du, D. (2022). Lyapunov function approach for approximation algorithm design and analysis: with applications in submodular maximization. arXiv preprint, arXiv:2205.12442.
Eckstein, J. and Bertsekas, D. P. (1992). On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Programming, 55(3, Ser. A):293-318.
Ehrhardt, M. J., Riis, E. S., Ringholm, T., and Schonlieb, C.-B. (2018). A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method. arXiv preprint, arXiv:1805.06444.
Franca, G., Robinson, D., and Vidal, R. (2018). ADMM and accelerated ADMM as continuous dynamical systems. In Proceedings of the 35th International Conference on Machine Learning, pages 1559-1567.
Gonzalez, O. (1996). Time integration and discrete Hamiltonian systems. J. Nonlinear Sci., 6(5):449-467.
Grimm, V., McLachlan, R. I., McLaren, D. I., Quispel, G. R. W., and Schonlieb, C.-B. (2017). Discrete gradient methods for solving variational image regularisation models. J. Phys. A, 50(29):295201, 21.
Itoh, T. and Abe, K. (1988). Hamiltonian-conserving discrete canonical equations based on variational difference quotients. J. Comput. Phys., 76(1):85-102.
Karimi, S. and Vavasis, S. A. (2016). A unified convergence bound for conjugate gradient and accelerated gradient. arXiv preprint, arXiv:1605.00320.
Krichene, W., Bayen, A., and Bartlett, P. L. (2015). Accelerated mirror descent in continuous and discrete time. In Advances in Neural Information Processing Systems, volume 28.
Luo, H. and Chen, L. (2022). From differential equation solvers to accelerated first-order methods for convex optimization. Math. Program., 195:735-781.
McLachlan, R. I., Quispel, G. R. W., and Robidoux, N. (1999). Geometric integration using discrete gradients. *R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci.*, 357(1754):1021-1045.
Miyatake, Y., Sogabe, T., and Zhang, S.-L. (2018). On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems. J. Comput. Appl. Math., 342:58-69.
Nesterov, Y. (2018). Lectures on convex optimization, volume 137 of Springer Optimization and Its Applications. Springer, Cham.