Title of Chapter/Section
A projection-type algorithm for pseudo-monotone non-Lipschitzian multivalued variational inequalities
Title of Book
Generalized Convexity and Generalized Monotonicity
Editor(s) of Book
Hadjisavvas, N., Kol´osi, S., Schaible, S.
Mathematics and Computer Science
Place of Publication
Year of Publication
Series (if applicable)
Nonconvex Optim. Appl.
Series Volume (if applicable)
113 - 129
We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, closed, lower hemicontinuous, and bounded on each bounded subset (it is not necessarily continuous). Some numerical test problems are implemented by using MATLAB with encouraging effectiveness.
Bao, T. Q.; Khanh, P. Q. A projection-type algorithm for pseudomonotone nonlipschitzian multivalued variational inequalities. Generalized convexity, generalized monotonicity and applications, 113–129, Nonconvex Optim. Appl., 77, Springer, New York, 2005.