A Projection-type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities
نویسندگان
چکیده
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.
منابع مشابه
Multivalued Variational Inequalities with DJ-Pseudomonotone Mappings in Reflexive Banach Spaces
and Applied Analysis 3 the multivalued projection for K; (2) ∇g ⋆ (] ) ∈ K : ⟨∇g ⋆ (] ) − x, ∇g ⋆ (ω )
متن کاملProjection Iterative Methods for Multivalued General Variational Inequalities
In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...
متن کاملA modified two-layer iteration via a boundary point approach to generalized multivalued pseudomonotone mixed variational inequalities
Most mathematical models arising in stationary filtration processes as well as in the theory of soft shells can be described by single-valued or generalized multivalued pseudomonotone mixed variational inequalities with proper convex nondifferentiable functionals. Therefore, for finding the minimum norm solution of such inequalities, the current paper attempts to introduce a modified two-layer ...
متن کاملOn the Vector Variational-like Inequalities with Relaxed η-α Pseudomonotone Mappings
In this paper we introduce some new conditions of the solu- tions existence for variational-like inequalities with relaxed &eta-&alpha pseu- domonotone mappings in Banach spaces. The advantage of these new conditions is that they are easier to be veried than those that appear in some of the previous corresponding articles.
متن کاملA Class of Globally Convergent Algorithms for Pseudomonotone Variational Inequalities
We describe a fairly broad class of algorithms for solving variational inequalities, global convergence of which is based on the strategy of generating a hyperplane separating the current iterate from the solution set. The methods are shown to converge under very mild assumptions. Specifically, the problem mapping is only assumed to be continuous and pseudomonotone with respect to at least one ...
متن کامل