An extension of the auxiliary problem principle to nonsymmetric auxiliary operators

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1. [1] B. Baillon, G. Haddad: Quelques Propriétés des Opérateurs Angles-Bornés et n-cycliquement Monotones, Israel Journal of Mathematics, 26, 1977, 137-150. Zbl0352.47023MR500279
2. [2] V. Barbu, T. Precupanu: Convexity and Optimization in Banach Spaces, Mathematics and its applications, East European Series, D. Reidel Publishing Company, 1986. Zbl0594.49001MR860772
3. [3] L. Bregman: The Relaxation Method of Finding the Common Point of Convex Sets and its Application to the Solution of Problems in Convex Programming, U.S.S.R. Comput. Math. and Math. Phys., 7, 1967, 200-217. Zbl0186.23807MR215617
4. [4] H. Brezis: Opérateurs Maximaux Monotones, Lectures Notes 5, North-Holland, 1973. 
5. [5] Y. Censor, S.A. Zenios: Proximal Minimization Algorithm with D-Functions, Journal of Optimization Theory and Application, 73, 1992, 451-464. Zbl0794.90058MR1164803
6. [6] G. Chen, M. Teboulle: Convergence Analysis of a Proximal-like Minimization Algorithm using Bregman Functions, SIAM Journal of Optimization, 3, 1993, 538-543. Zbl0808.90103MR1230155
7. [7] G. Cohen: Optimization by Decomposition and Coordination: a Unified Approach, IEEE Transactions on Automatic Control, 23, 1978, 222-232. Zbl0391.90074MR479480
8. [8] G. Cohen: Auxiliary Problem Principle and Decomposition of Optimization Problems, Journal of Optimization Theory and Applications, 32, 1980, 277-305. Zbl0417.49046MR607601
9. [9] G. Cohen: Auxiliary Problem Principle Extended to Variational Inequalities, Journal of Optimization Theory and Applications, 59, 1988, 369-390. Zbl0628.90069MR974037
10. [10] G. Cohen: Décomposition et Coordination en Optimisation Déterministe Différentiable et Non Différentiable, Thesis Dissertation, University of Paris Dauphine, 1984. 
11. [11] J.C. Dunn: Convexity, Monotonicity and Gradient Process in Hilbert Spaces, Journal of Mathematical Analysis and Applications, 53, 1976, 145-158. Zbl0321.49025MR388176
12. [12] J. Eckstein: Nonlinear Proximal Point Algorithms using Bregman Functions, Math. Oper. Research, 18, 1993, 202-226. Zbl0807.47036MR1250114
13. [13] J. Eckstein, D.P. Bertsekas: On the Douglas-Rachford Splitting Method and the Proximal Point Algorithm for Maximal Monotone Operators, Mathematical Programming, 55, 1992, 293-318. Zbl0765.90073MR1168183
14. [14] D. Gabay: Applications of the Method of Multipliers to Variational Inequalities, in Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems, M. Fortin and R. Glowinski, eds., North-Holland, Amsterdam, 1983, 299-331. 
15. [15] J.-B. Hiriart-Urruty, C. Lemaréchal: Convex Analysis and Minimization Algorithms, Springer-Verlag, Berlin, Germany, 1993. Zbl0795.49002
16. [16] B. Lemaire: The Proximal Algorithm, in International Series of Numerical Mathematics, J.-P. Penot ed., Birkhäuser-Verlag, Basel, 87, 1989, 73-87. Zbl0692.90079
17. [17] P.-L. Lions, B. Mercier: Splitting Algorithm for the Sum of Two Nonlinear Operators, SIAM J. Numer. Anal., 16, 1979, 964-979. Zbl0426.65050MR551319
18. [18] F.J.R. Luque: Asymptotic Convergence Analysis of the Proximal Point Algorithm, SIAM Journal of Control and Optimization, 22, 1984, 277-293. Zbl0533.49028MR732428
19. [19] B. Martinet: Régularisation d'Inéquations Variationnelles par Approximations Successives, Revue d'Automatique, d'Informatique et de Recherche Opérationnelle, Série Rouge, 3, 1970, 154-159. Zbl0215.21103MR298899
20. [20] M.A. Mataoui: Contributions à la Décomposition et à l'Agrégation des Problèmes Variationnels, Thesis Dissertation, École des Mines de Paris, Paris, France, 1990. 
21. [21] J.-J. Moreau: Proximité et Dualité dans un Espace Hilbertien, Bull. Soc. Math. France, 93, 1965, 273-299. Zbl0136.12101MR201952
22. [22] M. Patriksson: A Unified Framework of Descent Algorithm for Nonlinear Programs and Variational Inequalities, Thesis Dissertation, Linköping University, 1993. 
23. [23] R.T. Rockafellar: Local Boundedness of Nonlinear Monotone Operators, Michigan Mathematics Journal, 16, 1969, 397-407. Zbl0175.45002MR253014
24. [24] R.T. Rockafellar: On the Maximality of Sums of Nonlinear Monotone Operators, Transactions of the American Mathematical Society, 149, 1970, 75-88. Zbl0222.47017MR282272
25. [25] R.T. Rockafellar: Monotone Operators and the Proximal Point Algorithm, SIAM Journal of Control and Optimization, 14, 1976, 877-898. Zbl0358.90053MR410483
26. [26] P. Tseng: Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities, SIAM Journal of Control and Optimization, 29, 1991, 119-138. Zbl0737.90048MR1088222
27. [27] K. Yosida: Functional Analysis, Springer-Verlag, 1964. 
28. [28] D. Zhu, P. Marcotte: New Classes of Generalized Monotonicity, Journal of Optimization Theory and Applications, 87, 1995, 457-471. Zbl0837.65067MR1358753