A Logarithmic-Quadratic Proximal Method for Variational Inequalities

Computational Optimization and Applications

Volumn 12, Issue 1-3, 1999, Pages 31-40

  Auslender, Alfred ^a   Teboulle, Marc ^b   Ben Tiba, Sami ^a  

^a ECOLE POLYTECHNIQUE   (France)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Global convergence; Interior point methods; Maximal monotone operators; Nonlinear complementarity; Proximal like methods; Saddle point computation; Variational inequalities

Indexed keywords

EID: 0002434986     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1007/978-1-4615-5197-3_3     Document Type: Article

References (16)

1. A. Auslender and M. Haddou, "An interior proximal method for convex linearly constrained problems and its extension to variational inequalities," Mathematical Programming, vol. 71, pp. 77-100, 1995.
2. A. Auslender, M. Teboulle, and S. Ben-Tiba, "Interior proximal and multiplier methods based on second order homogeneous functionals," Submitted 1998.
3. R.D. Bruck, "An iterative solution of a variational inequality for certain monotone operators in Hilbert space," Bulletin of the American Math. Soc., vol. 81, pp. 890-892, 1975 (With corrigendum, in vol. 82, p. 353, 1976).
4. R.S. Burachik and A.N. Iusem, "A generalized proximal point algorithm for the variational inequality problem in a Hilbert space," SIAM Journal on Optimization, vol. 8, pp. 197-216, 1998.
5. Y. Censor, A.N. Iusem, and S.A. Zenios, "An interior-point method with Bregman functions for the variational inequality problem with paramonotone operators," Working paper, University of Haifa, 1994.
6. J. Eckstein, "Approximate iterations in Bregman-function-based proximal algorithms," RRR, 12-96, January 97, Rutgers University.
7. Z.Q. Luo and P. Tseng, "Error bounds and convergence analysis of feasible descent methods: A general approach," Annals of Operations Research, vol. 46, pp. 157-178, 1993.
8. B. Martinet, "Regularisation d'inéquations variationnelles par approximations successives, Revue Francaise d'Automatique et Informatique recherche Opérationnelle," vol. 4, pp. 154-159, 1970.
9. A. Nemirovski, "On self-concordant convex-concave functions," Research Report 3/97, Optimization Laboratory Faculty of Industrial Engineering and Management, Technion Haifa.
10. Y. Nesterov and A. Nemirovski, Interior Point Polynomial Algorithms in Convex Programming, SIAM Publications: Philadelphia, PA, 1994.
11. B.T. Polyak, Introduction to Optimization, Optimization Software Inc.: New York, 1987.
12. R.T. Rockafellar, "On the maximality of sums of nonlinear monotone operators, Transactions of the American Mathematical Society," vol. 149, pp. 75-88, 1970.
13. R.T. Rockafellar, Convex Analysis, Princeton University Press: Princeton, NJ, 1970.
14. R.T. Rockafellar, "Monotone operators and the proximal point algorithm," SIAM J. of Control and Optimization, vol. 14, pp. 877-898, 1976.
15. R.T. Rockafellar, "Augmented Lagrangians and applications of the proximal point algorithm in convex programming," Mathematics of Operations Research, vol. 1, pp. 97-116, 1976.
16. M. Teboulle, "Convergence of proximal-like algorithms," SIAM J. of Optimization, vol. 7, pp. 1069-1083, 1997.