References
- Attouch H, Briceño-Arias LM, Combettes PL. A parallel splitting method for coupled monotone inclusions. SIAM J. Control Optim. 2010;48:3246–3270.
- Attouch H, Maingé PE. Asymptotic behavior of second order dissipative evolution equations combining potential with non-potential effects. ESAIM Control Optim. Calc. Var. 2011;17:836–857.
- Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York (NY): Springer; 2011.
- Zhu DL, Marcotte P. Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. J. Optim. 1996;6:714–726.
- Attouch H, Svaiter BF. A continuous dynamical Newton-like approach to solving monotone inclusions. SIAM J. Control Optim. 2011;49:574–598.
- Abbas B, Attouch H, Svaiter BF. Newton-like dynamics and forward-backward methods for structured monotone inclusions in Hilbert spaces. J. Optim. Theory Appl. 2014;161:331–360.
- Bruck RE. Asymptotic convergence of nonlinear contraction semigroups in Hilbert spaces. J. Funct. Anal. 1975;18:15–26.
- Antipin AS. Minimization of convex functions on convex sets by means of differential equations. Differ. Equ. 2010;30:3246–3270.
- Bolte J. Continuous gradient projection method in Hilbert spaces. J. Optim. Theory Appl. 2003;119:235–259.
- Attouch H, Peypouquet J, Redont P. Forward-backward and backward-forward algorithms for structured monotone inclusions, working paper; 2014.
- Attouch H, Redont P, Svaiter BF. Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces. J. Optim. Theory Appl. 2013;157:624–650.
- Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert [Maximal monotone operators and semi-groups of contractions in Hilbert spaces]. New York (NY): North-Holland/Elsevier; 1973.
- Baillon J-B, Haddad G. Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones [Some properties of angle-bounded operators, and n-cyclically monotone operators]. Israël J. Math. 1977;26:137–150.
- Combettes PL. Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization. 2004;53:475–504.
- Attouch H, Théra M. A general duality principle for the sum of two operators. J. Convex Anal. 1996;3:1–24.
- Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 1967;73:591–597.
- Attouch H, Peypouquet J, Redont P. A dynamical approach to an inertial forward-backward algorithm for convex minimization. SIAM J. Optim. 2014;24:232–256.
- Baillon J-B, Brézis H. Une remarque sur le comportement asymptotique des semi-groupes non linéaires [A remark on the asymptotic behavior of nonlinear semigroups]. Houston J. Math. 1976;2:5–7.
- Baillon J-B. Un exemple concernant le comportement asymptotique de la solution du probléme du⁄dt + ∂φ(u) ∋ 0 [An example on the asymptotic behavior of the solution of the problem du⁄dt + ∂φ(u) ∋ 0]. J. Funct. Anal. 1978;28:369–376.
- Daniilidis A. Gradient dynamical systems, tame optimization and applications. Lecture notes, spring school on variational analysis. Paseky nad Jizerou, Czech Republic; April 20–24, 2009.
- Lions PL, Mercier B. Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 1979;16:964–979.
- Attouch H, Bolte J, Svaiter BF. Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods. Math. Prog. 2013;137:91–129.
- Nesterov YE. A method for solving the convex programming problem with convergence rate O(1/k2). Dokl. Akad. Nauk SSSR. 1983;269:543–547.
- Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2009;2:183–202.
- Attouch H, Goudou X. A continuous gradient-like dynamical approach to Pareto-optimization in Hilbert spaces. Set-Valued Var. Anal. 2014;22:189–219.
- Attouch H, Cominetti R. A dynamical approach to convex minimization coupling approximation with the steepest descent method. J. Differ. Equ. 1996;128:519–540.
- Attouch H, Czarnecki M-O. Asymptotic behavior of coupled dynamical systems with multiscale aspects. J. Differ. Equ. 2010;248:1315–1344.
- Baillon J-B, Cominetti R. A convergence result for non-autonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming. J. Funct. Anal. 2001;187:263–273.
- Bian W, Xue X. Asymptotic behavior analysis on multivalued evolution inclusion with projection in Hilbert space. Optimization. 2013. doi:10.1080/02331934.2013.811668.
- Cabot A. The steepest descent dynamical system with control. Applications to constrained minimization. ESAIM Control Optim. Calc. Var. 2004;10:243–258.
- Combettes PL, Hirstoaga SA. Approximating curves for nonexpansive and monotone operators. J. Convex Anal. 2006;13:633–646.
- Cominetti R, Peypouquet J, Sorin S. Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization. J. Differ. Equ. 2008;245:3753–3763.
- Hirstoaga SA. Approximation et résolution de problèmes d’équilibre, de point fixe et d’inclusion monotone [Approximation and numerical solution of equilibrium, fixed-point and monotone inclusion problems] [PhD thesis]. Paris VI: Université Pierre et Marie Curie; 2006.
- Attouch H, Czarnecki M-O, Peypouquet J. Coupling forward-backward with penalty schemes and parallel splitting for constrained variational inequalities. SIAM J. Optim. 2011;21:1251–1274.