Alternating proximal algorithms for linearly constrained variational inequalities: Application to domain decomposition for PDE’s
Tài liệu tham khảo
A. Cabot, P. Frankel, Alternating proximal algorithms with asymptotically vanishing coupling. Application to domain decomposition for PDE’s, Optimization (in press).
Attouch, 2007, A new class of alternating proximal minimization algorithms with costs-to-move, SIAM J. Optim., 18, 1061, 10.1137/060657248
Attouch, 2008, Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE’s, J. Convex Anal., 15, 485
Acker, 1980, Convergence d’un schéma de minimisation alternée, Ann. Fac. Sci. Toulouse Math. (5), 2, 1, 10.5802/afst.541
Bauschke, 2005, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal., 60, 283, 10.1016/j.na.2004.07.054
Attouch, 2011, Prox-penalization and splitting methods for constrained variational problems, SIAM J. Optim., 21, 149, 10.1137/100789464
Cabot, 2005, Proximal point algorithm controlled by a slowly vanishing term: applications to hierarchical minimization, SIAM J. Optim., 15, 555, 10.1137/S105262340343467X
Auslender, 1987, Penalty-proximal methods in convex programming, J. Optim. Theory Appl., 55, 1, 10.1007/BF00939042
Attouch, 2010, Asymptotic behavior of coupled dynamical systems with multiscale aspects, J. Differential Equations, 248, 1315, 10.1016/j.jde.2009.06.014
Cominetti, 2002, Coupling general penalty schemes for convex programming with the steepest descent method and the proximal point algorithm, SIAM J. Optim., 13, 745, 10.1137/S1052623401397242
Brézis, 1972, Opérateurs maximaux monotones dans les espaces de Hilbert et équations d’évolution, vol. 5
Passty, 1979, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72, 383, 10.1016/0022-247X(79)90234-8
Ekeland, 1999, Convex analysis and variational problems, SIAM Classics Appl. Math., 28
Opial, 1967, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73, 591, 10.1090/S0002-9904-1967-11761-0
Rockafellar, 1998
J.J. Moreau, Fonctionnelles convexes, Cours Collège de France 1967, new edition CNR, Facoltà di Ingegneria di Roma, 2003.
Rockafellar, 1970
Attouch, 1986, Duality for the sum of convex functions in general Banach spaces, 125
Rockafellar, 1976, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14, 877, 10.1137/0314056
Auslender, 1987, Numerical methods for nondifferentiable convex optimization, Math. Program. Stud., 30, 102, 10.1007/BFb0121157
Solodov, 1999, An inexact hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Anal., 7, 323, 10.1023/A:1008777829180
Álvarez, 2010, Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces, Nonlinear Anal., 73, 3018, 10.1016/j.na.2010.06.070
Polyak, 1987
Álvarez, 2002, Primal and dual convergence of a proximal point exponential penalty method for linear programming, Math. Program., 93, 87, 10.1007/s10107-002-0295-0
Attouch, 2002, Asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria, J. Differential Equations, 179, 278, 10.1006/jdeq.2001.4034
Baillon, 2001, 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., 187, 263, 10.1006/jfan.2001.3828
Brézis, 1978, Produits infinis de résolvantes, Israel J. Math., 29, 329, 10.1007/BF02761171
Attouch, 2006, Variational analysis in Sobolev and BV spaces. Applications to PDE’s and optimization, vol. 6
Brézis, 1999
Lions, 1972, Non-homogeneous boundary value problems and applications
Raviart, 1993
Agmon, 1959, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12, 623, 10.1002/cpa.3160120405
Agmon, 1964, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17, 35, 10.1002/cpa.3160170104
Gilbarg, 1977
Azé, 1997
Marschall, 1987, The trace of Sobolev–Slobodeckij spaces on Lipschitz domains, Manuscripta Math., 58, 47, 10.1007/BF01169082
Adams, 1975
Attouch, 2009, Augmented Lagrangian and proximal alternating direction methods of multipliers in Hilbert spaces. Applications to games, PDE’s and control, Pac. J. Optim., 5, 17