A new alternating direction method for co-coercive variational inequality problems

Computers and Mathematics with Applications

Volumn 57, Issue 7, 2009, Pages 1168-1178

  Zhang, Wenxing ^a   Han, Deren ^a  

^a NANJING NORMAL UNIVERSITY   (China)

Author keywords

Alternating direction methods; Co coercive mappings; Projection methods; Variational inequality problems

Indexed keywords

COERCIVE FORCE; SITE SELECTION;

ALTERNATING DIRECTION METHODS; CO-COERCIVE MAPPINGS; DESCENT METHODS; FEASIBLE SETS; NUMERICAL RESULTS; OPERATIONAL RESEARCHES; OPTIMIZATION THEORIES; PROJECTION METHODS; SYSTEM OF LINEAR EQUATIONS; VARIATIONAL INEQUALITIES; VARIATIONAL INEQUALITY PROBLEMS;

VARIATIONAL TECHNIQUES;

EID: 61749087247     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.09.049     Document Type: Article

References (16)

1. Nagurney A. Network Economics, A Variational Inequality Approach (1993), Kluwer Academics Publishers, Dordrect
2. Facchinei F., and Pang J.S. Finite-Dimensional Variational Inequalities and Complementarity Problems vols. I and II (2003), Springer Verlag, Berlin
3. Gabay D. Applications of the method of multipliers to variational inequalities. In: Fortin M., and Glowinski R. (Eds). Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems (1983), North-Holland, Amsterdam 299-311
4. Gabay D., and Mercier B. A dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Computers and Mathematics with Applications 2 1 (1976) 17-40
5. Fortin M., and Glowinski R. Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems (1983), North-Holland, Amsterdam
6. Glowinski R. Numerical Methods for Nonlinear Variational Problems (1984), Springer-Verlag, New York
7. R. Glowinski, P. Le Tallec, Augmented Lagrangian and operator-splitting method in nonlinear mechanics, SIAM Studies in Applied Mathematics, Philadelphia, PA, 1989
8. He B.S., and Zhou J. A modified alternating direction method for convex minimization problems. Applied Mathematics Letters 13 (2000) 123-130
9. Han D.R., and Lo H.K. A new stepsize rule in He and Zhou's alternating direction method. Applied Mathematics Letters 15 (2002) 181-185
10. Han D.R., and Lo H.K. A new alternating direction method for a class of nonlinear variational inequality problems. Journal of Optimization Theory and Applications 112 3 (2002) 549-560
11. Han D.R. A modified alternating direction method for variational inequality problems. Applied Mathematics and Optimization 45 (2002) 63-74
12. Zhu D.L., and Marcotte P. Cocoercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM Journal on Optimization 6 (1996) 714-726
13. Cohen G. Auxiliary problem principle extended to variational inequalities. Journal of Optimization, Theory and Applications 59 (1988) 325-333
14. Han D.R., and Lo H.K. Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities. European Journal of Operational Research 159 (2004) 529-544
15. Li M., Liao L.Z., and Yuan X.M. A modified descent projection method for co-coercive variational inequalities. European Journal of Operational Research 189 2 (2008) 310-323
16. Eaves B.C. Computing stationary points. Mathematical Programming Study 7 (1978) 1-14