In this paper, we consider a generalized nonlinear variational inequality problem involving single valued and multivalued nonlinear operators. We also study criteria of its solvability. Iterative methods for approximate solution are also proposed and a convergence result is established. Further, we study iterative methods for finding common element of fixed point set of nonexpansive mapping and...

We consider control problems for the variational inequality describing a single degree of freedom elasto-plastic oscillator. We are particularly interested in finding the ”critical excitation”, i.e., the lowest energy input excitation that drives the system between the prescribed initial and final states within a given time span. This is a control problem for a state evolution described by a va...

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces. We prove that the whole sequence of iterates converges strongly to a solution of the variational inequality. The method uses only two projections onto the feasible set in each iteration in contrast to other strongly convergent algorithms which either require plenty of projection...

In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated ...

Among the central concerns in mathematical finance is the evaluation of American options. An American option gives the holder the right but not the obligation to buy or sell a certain financial asset within a certain time-frame, for a certain strike price. The valuation of American options is formulated as an optimal stopping problem. If the stock price is modelled by a geometric Brownian motio...

An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.

Sensitivity analysis of solution for variational inequalities and variational inclusions has been studied by many authors via quite different technique. See 1–7 and the reference therein . In 2004, Agarwal et al. 1 introduced and studied the following problem which is called the system of parametric generalized nonlinear mixed quasi variational inclusions. Let H be a real Hilbert space endowed ...

We provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index formula can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map (INM) property, which is implied by strong...

In this paper we present a penalty method for solving a complementarity problem involving 2nd-order nonlinear parabolic differential operators. In this work we first rewrite the complementarity problem as a nonlinear variational inequality. Then, we define a nonlinear parabolic partial differential equation (PDE) approximating the variational inequality using a power penalty term with a penalty...