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Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems.
1905
Earlier work this paper cites.
T. H. Gronwall, “Note on the derivatives with respect to a parameter of the solutions of a system of differential equations,” Ann. of Math
1919
Earlier work this paper cites.
R. Bellman, “The stability of solutions of linear differential equations,” Duke Math. J
1943
Earlier work this paper cites.
B. T. Polyak, “Some methods of speeding up the convergence of iteration methods,” USSR Comp. Math. and Math. Phys
1964
Earlier work this paper cites.
R. E. O’Malley, “Topics in singular perturbations,” Advances in Mathematics
1968
Earlier work this paper cites.
R. T. Rockafellar, “Generalized Hamiltonian Equations for Convex Problems of Lagrange,” Pacific J. Math
1970
Earlier work this paper cites.
R. Glowinski and A. Marroco, “Sur l’approximation, par él’ements finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de probèmes de Dirichlet non linéaires,” ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
1975
Earlier work this paper cites.
D. Gabay and B. Mercier, “A dual algorithm for the solution of nonlinear variational problems via finite element approximations,” Comp. Math. App
1976
Earlier work this paper cites.
D. P. Bertsekas, “On penalty and multiplier methods for constrained minimization,” SIAM J. Control and Optimization
1976
Earlier work this paper cites.
H. Yamashita, “A differential equation approach to nonlinear programming,” Math. Program
1980
Earlier work this paper cites.
Y. Nesterov, “A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2}) ,” Soviet Mathematics Doklady
1983
Earlier work this paper cites.
Springer-Verlag, 1990
E. Zeidler, Nonlinear Functional Analysis and its Applications, II/B: Nonlinear Monotone Operators · 1990
Earlier work this paper cites.
P. Lowen and R. T. Rockafellar, “The adjoint arc in nonsmooth optimization,” Trans. Amer. Math. Soc
1991
Earlier work this paper cites.
A. Dontchev and F. Lempio, “Difference methods for differential inclusions: a survey,” SIAM Review
1992
Earlier work this paper cites.
J. Eckstein, “Parallel Alternating Direction Multiplier Decomposition of Convex Programs,” J. Optimization Theory and Applications
1994
Earlier work this paper cites.
P. Lowen and R. T. Rockafellar, “Optimal control of unbounded differential inclusions,” SIAM J. Control Opt
1994
Earlier work this paper cites.
F. Lempio, “Euler’s method revisited,” Trudy Mat. Inst. Steklov
1995
Earlier work this paper cites.
Princeton University Press, 1996
R. T. Rockafellar, Convex Analysis · 1996
Earlier work this paper cites.
A. Ioffe, “Euler-Lagrange and Hamiltonian formalisms in dynamic optimization,” Trans. Amer. Math. Soc
1997
Cited alongside, same era.
J. Eckstein and M. C. Ferris, “Operator-splitting methods for monotone affine variational inequalities, with a paralell application to optimal control,” INFORMS J. Computing
1998
Cited alongside, same era.
J. Schropp and I. Singer, “A dynamical systems approach to constrained minimization,” Num. Func. Anal. and Opt
2000
Cited alongside, same era.
Springer, 2000
J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization · 2000
Cited alongside, same era.
Springer, 2004
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course · 2004
Cited alongside, same era.
Springer, 2005
F. Verhulst, Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics · 2005
J. Rieger, “Semi-implicit euler schemes for ordinary differential inclusions,” SIAM J. Numer. Anal
2014
Later among the works it cites.
J. Eckstein and W. Yao, “Understanding the convergence of the alternating direction method of multipliers: Theoretical and computational perspectives.” 2015
2015
Later among the works it cites.
Springer, 2015
C. Kuehn, Multiple Time Scale Dynamics · 2015
Later among the works it cites.
W. Su, S. Boyd, and E. J. Candès, “A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights,” J. Machine Learning Research
2016
Later among the works it cites.
A. Wibisono, A. C. Wilson, and M. I. Jordan, “A variational perspective on accelerated methods in optimization,” Proc. Nat. Acad. Sci
2016
Later among the works it cites.
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Cited alongside, same era.
Springer, 2006
C. M. Bishop, Pattern Recognition and Machine Learning · 2006
Cited alongside, same era.
H. Zou, T. Hastie, and R. Tibshirani, “Sparse principal component analysis,” J. Comput. and Graph. Stat
2006
Cited alongside, same era.
A. d’Aspremont, L. E. Ghaoui, , M. I. Jordan, and G. R. G. Lanckriet, “A direct formulation for sparse pca using semidefinite programming,” SIAM Review
2007
Cited alongside, same era.
S.-J. Kim, K. Koh, S. Boyd, and D. Gorinevsky, “ ℓ 1 \ell_{1} trend filtering,” SIAM Review
2009
Cited alongside, same era.
W.-J. Beyn and J. Rieger, “The implicit euler scheme for one-sided lipschitz differential inclusions,” Discrete and Continuous Dynamical Systems Series B
2010
Cited alongside, same era.
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends in Machine Learning
2011
Cited alongside, same era.
W. Deng and W. Yin, “On the global and linear convergence of the generalized alternating direction method of multipliers,” J. Sci. Comp
2016
Later among the works it cites.
I. T. Jolliffe and J. Cadima, “Principal component analysis: a review and recent developments,” Phil. Trans. R. Soc. A
2016
Later among the works it cites.
M. Hong and Z.-Q. Luo, “On the linear convergence of the alternating direction method of multipliers,” Math. Program
2017
Later among the works it cites.
P. P. Markopoulos, S. Kundu, S. Chamadia, and D. A. Pados, “Efficient l1-norm principal-component analysis via bit flipping,” IEEE Trans. on Signal Processing
2017
Later among the works it cites.
2018
Closest in time.
I. Necoara, Y. Nesterov, and F. Glineur, “Linear convergence of first order methods for non-strongly convex optimization,” Math. Program
2019
Closest in time.
P. Casau, R. Cunha, R. G. Sanfelice, and C. Silvestre, “Hybrid control for robust and global tracking on smooth manifolds,” IEEE Trans. on Automatic Control
2020
Closest in time.
G. França, J. Sulam, D. P. Robinson, and R. Vidal, “Conformal symplectic and relativistic optimization,” J. Stat. Mech
2020
Closest in time.
G. França, M. I. Jordan, and R. Vidal, “On dissipative symplectic integration with applications to gradient-based optimization,” J. Stat. Mech
2021
Closest in time.
G. França, D. P. Robinson, and R. Vidal, “Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization,” Phys. Rev. E
2021
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K. Camlibel, L. Iannelli, and A. Tanwani, “Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators,” Math. Program
2021
Closest in time.
B. Shi, S. S. Du, M. I. Jordan, and W. J. Su, “Understanding the acceleration phenomenon via high-resolution differential equations,” Math. Prog
2022
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