Solving a class of asymmetric variational inequalities by a new alternating direction method

Computers and Mathematics with Applications

Volumn 40, Issue 8, 2000, Pages 927-937

  Wang, Shengli ^a   Yang, Hai ^b   He, Bingsheng ^a  

^a NANJING UNIVERSITY   (China)

^b Dept Civ Eng Hong Kong Univ S ^*  (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

ALTERNATING DIRECTION METHOD; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 0342955014     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(00)85004-X     Document Type: Article

References (29)

1. Dafermos S. Traffic equilibrium and variational inequalities. Transportation Science. 14:1980;42-54.
2. Lemke C.E. Bimatrix equilibrium points and mathematical programming. Management Science. 11:1965;681-689.
3. Nagurney A. Network Economics, A Variational Inequality Approach. 1993;Kluwer Academic, Dordrecht.
4. Nagurney A., Ramanujam P. Transportation network policy modeling with goal targets and generalized penalty functions. Transportation Science. 30:1996;3-13.
5. Taji K., Fukushima M., Ibaraki T. A globally convergent Newton method for solving strongly monotone variational inequalities. Mathematical Programming. 58:1993;369-383.
6. Harker P.T., Pang J.S. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming. 48:1990;161-220.
7. Harker P.T., Xiao B. Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach. Mathematical Programming. 48:1990;339-357.
8. He B.S. A projection and contraction method for a class of linear complementarity problem and its application in convex quadratic programming. Applied Mathematics and Optimization. 25:1992;247-262.
9. He B.S. A new method for a class of linear variational inequalities. Mathematical Programming. 66:1994;137-144.
10. He B.S. A class of projection and contraction method for monotone variational inequalities. Appl. Mathematics and Optimization. 35:1997;69-76.
11. Isac G. Complementarity Problems, Lecture Notes in Mathematics. 1528:1992;Springer-Verlag, Berlin.
12. Nagurney A., Thore S., Pan J. Spatial market policy modeling with goal targets. Operations Research. 44:1996;393-406.
13. Noor M.A. Some recent advances in variational inequalities, Part I. Basic concepts. New Zealand J. Math. 26:1997;53-80.
14. Noor M.A. Some recent advances in variational inequalities, Part II. Other concepts. New Zealand J. Math. 26:1997;229-255.
15. Fukushima M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Mathematical Programming. 53:1992;99-110.
16. Noor M.A. An implicit method for mixed variational inequalities. Appl. Math. Lett. 11:(4):1998;109-113.
17. Gabay D. Applications of the method of multipliers to variational inequalities. Fortin M., Glowinsky R. Augmented Lagrange Methods: Applications to Solution of Boundary-Valued Problems. 1983;299-331 North Holland, Amsterdam, the Netherlands.
18. Gabay D., Mercier B. A dual algorithm for the solution of nonlinear variation problems via finite-element approximations. Computers Math. Applic. 2:(1):1976;17-40.
19. Glowinski R. Numerical Methods for Nonlinear Variational Problems. 1984;Springer-Verlag, New York.
20. Glowinski R., Lions J.L., Tremolieres R. Numerical Analysis of Variational Inequalities. 1981;North-Holland, Amsterdam.
21. He B.S., Yang H. Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. Operation Research Letters. 23:1998;151-161.
22. Bazaraa M.S., Shetty C.M. Nonlinear Programming Theory and Algorithm. 1979;438-447 John Wiley and Sons.
23. Dennis J.E., Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. 1983;Prentice-Hall, Englewood Cliffs, NJ.
24. Fletcher R. Practical Methods of Optimization. 1985;Wiley, New York.
25. Ortega J.M., Rheiboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables. 1970;Academic Press, New York.
26. Rice J.R. Second Edition Numerical Methods, Software, and Analysis. 1993;Academic Press, Harcourt Brace Jovanovich.
27. Pang J.S. Error bounds in mathematical programming. Mathematical Programming. 79:1997;299-332.
28. Yang H. Multiple equilibrium behaviors and advanced traveler information systems with endogenous market penetration. Transportation Research B. 32:1998;205-218.
29. He B.S. Inexact implicit method for general monotone variational inequalities. Mathematical Programming. 86:1999;199-217.