A descent algorithm for solving monotone variational inequalities and monotone complementarity problems

The paper provides a descent algorithm for solving certain monotone variational inequalities and shows how this algorithm may be used for solving certain monotone complementarity problems. Convergence is proved under natural monotonicity and smoothness conditions; neither symmetry nor strict monotonicity is required.

[1]  F. Browder.  Nonlinear monotone operators and convex sets in Banach spaces , 1965 .

[2]  F. Browder.  Existence and approximation of solutions of nonlinear variational inequalities. , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[3]  M. Sibony.  Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone , 1970 .

[4]  S. Karamardian,et al.  The complementarity problem , 1972, Math. Program..

[5]  O. Mangasarian.  Solution of symmetric linear complementarity problems by iterative methods , 1977 .

[6]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[7]  R. Cottle.  Numerical methods for complementarity problems in engineering and applied science , 1979 .

[8]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[9]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[10]  B. Ahn.  Solution of nonsymmetric linear complementarity problems by iterative methods , 1981 .

[11]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[12]  D. Bertsekas,et al.  Projection methods for variational inequalities with application to the traffic assignment problem , 1982 .

[13]  Mike J. Smith.  The existence and calculation of traffic equilibria , 1983 .

[14]  R. Glowinski,et al.  Numerical Methods for Nonlinear Variational Problems , 1985 .