References
- Hestenes MR. Multiplier and gradient methods. In: Zadeh LA, Neustadt LW, Balakrishnan AV, editors. Computing methods in optimization problems-2; New York: Academic Press; 1969.
- Hestenes MR. Multiplier and gradient methods. J Optim Theory Appl. 1969;4:303–320. doi: 10.1007/BF00927673
- Powell MJD. A method for nonlinear constraints in minimization problems. In: Fletcher, editor. Optimization. New York; Academic Press; 1972.
- Rockafellar RT. The multiplier method of Hestenes and Powell applied to convex programming. J Optim Theory Appl. 1973;12:555–562. doi: 10.1007/BF00934777
- Rockafellar RT. Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math Oper Res. 1976;1(2):97–116. doi: 10.1287/moor.1.2.97
- Rockafellar RT. Monotone operators and the proximal point algorithm. SIAM J Control Optim. 1976;14(5):877–898. doi: 10.1137/0314056
- Monteiro RDC, Svaiter BF. Iteration-complexity of a Newton proximal extragradient method for monotone variational inequalities and inclusion problems. SIAM J Optim. 2012;22(3):914–935. doi: 10.1137/11083085X
- Solodov MV, Svaiter BF. A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set-Valued Anal. 1999;7(4): 323–345. doi: 10.1023/A:1008777829180
- Svaiter BF. Complexity of the relaxed hybrid proximal-extragradient method under the large-step condition. Preprint A766/2015, IMPA – Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ Brasil 22460-320, 2015.
- Nesterov Yu, Polyak BT. Cubic regularization of Newton method and its global performance. Math Program. 2006;108(1, Ser. A):177–205. doi: 10.1007/s10107-006-0706-8
- Dong Y. The proximal point algorithm revisited. J Optim Theory Appl. 2014;161(2): 478–489. doi: 10.1007/s10957-013-0351-3
- Dong Y. Comments on ‘The proximal point algorithm revisited’ [MR3193802]. J Optim Theory Appl. 2015;166(1):343–349. doi: 10.1007/s10957-014-0685-5
- Sicre MR, Svaiter BF. An O(1/k3/2) hybrid proximal extragradient primal-dual interior point method for non-linear monotone mixed complementarity problems. Comput Appl Math. 2017;37:1847–1876. doi: 10.1007/s40314-017-0425-1
- Minty GJ. Monotone (nonlinear) operators in Hilbert space. Duke Math J. 1962;29: 341–346. doi: 10.1215/S0012-7094-62-02933-2
- Solodov MV, Svaiter BF. A hybrid projection-proximal point algorithm. J Convex Anal. 1999;6(1):59–70.
- Burachik RS, Iusem AN, Svaiter BF. Enlargement of monotone operators with applications to variational inequalities. Set-Valued Anal. 1997;5(2):159–180. doi: 10.1023/A:1008615624787
- Solodov MV, Svaiter BF. A unified framework for some inexact proximal point algorithms. Numer Funct Anal Optim. 2001;22(7–8):1013–1035. doi: 10.1081/NFA-100108320
- Monteiro RDC, Svaiter BF. Complexity of variants of Tseng's modified F-B splitting and Korpelevich's methods for hemivariational inequalities with applications to saddle point and convex optimization problems. SIAM J Optim. 2010;21:1688–1720. doi: 10.1137/100801652
- Monteiro RDC, Svaiter BF. On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean. SIAM J Optim. 2010;20:2755–2787. doi: 10.1137/090753127
- Monteiro RDC, Svaiter BF. Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers. SIAM J Optim. 2013;23(1):475–507. doi: 10.1137/110849468
- Solodov MV, Svaiter BF. A truly globally convergent Newton-type method for the monotone nonlinear complementarity problem. SIAM J Optim. 2000;10(2):605–625. (electronic) doi: 10.1137/S1052623498337546
- Solodov MV, Svaiter BF. A new proximal-based globalization strategy for the Josephy-Newton method for variational inequalities. Optim Methods Software. 2002;17(5):965–983. doi: 10.1080/1055678021000056563
- Solodov MV, Svaiter BF. Error bounds for proximal point subproblems and associated inexact proximal point algorithms. Math Program. 2000;88(2, Ser. B):371–389. Error bounds in mathematical programming (Kowloon, 1998). doi: 10.1007/s101070050022
- Brøndsted A, Rockafellar RT. On the subdifferentiability of convex functions. Proc Am Math Soc. 1965;16:605–611. doi: 10.1090/S0002-9939-1965-0178103-8