Algorithms for General Monotone Mixed Variational Inequalities

Iterative Algorithms for General Multivalued Variational Inequalities

and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...

On Two Iterative Methods for Mixed Monotone Variational Inequalities

A mixed monotone variational inequality MMVI problem in a Hilbert space H is formulated to find a point u∗ ∈ H such that 〈Tu∗, v − u∗〉 φ v − φ u∗ ≥ 0 for all v ∈ H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function onH. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the ...

Parametric Extended General Mixed Variational Inequalities

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational ...

Monotone Iterations for Eliptic Variational Inequalities

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...