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

Document Type

Book Section/Chapter

Place of Publication

New York



Year of Publication


Series (if applicable)

Nonconvex Optim. Appl.

Series Volume (if applicable)


Page Range

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.