For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely manymaximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mecha...

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We also develop a s...

We prove existence, uniqueness, and regularity properties for a solution u of the Bellman-Dirichlet equation of dynamic programming: (1) max {I]u+f i} =0 in (2 i = 1 , 2 u=O on 092, where D and L 2 are two second order, uniformly elliptic operators. The method of proof is to rephrase (1) as a variational inequality for the operator K = L 2 (D)1 in L2(O) and to invoke known existence theorems. F...

In this paper we study the class of differential variational inequality(DVI) in a finite-dimension Euclidean space <n, which is the following form ẋ(t) = f(t, x(t)) + B(t, x(t))u(t) , x(0) = x0 ∈ <n 0 ≤ (ũ− u(t))T [G(t, x(t)) + F (u(t))] for almost all ũ ∈ K u(t) ∈ K We study stability and perturbation of the DVI under the OSL condition. Besides, we establish a Prior Bound Theorem, which is a u...

This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable functions. The importance of tilt stability has been well recognized from both theoretical and numerical perspectives of optimization, and this area of research has drawn much attent...

In this work, we are concerned with the finite element approximation for the stationary power law Stokes equations driven by nonlinear slip boundary conditions of ‘friction type’. After the formulation of the problem as mixed variational inequality of second kind, it is shown by application of a variant of Babuska– Brezzi’s theory for mixed problems that convergence of the finite element approx...

We propose a new solving approach for shape optimization (optimal design problem) of elastic solids in contact. As the equilibrium of a solid in contact is a solution of constrained minimization problem for the body energy functional (or an variational inequality), we can consider our optimization problem as a classical bilevel mathematical program (or a generalized bilevel programming problem)...

We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine Hadamard manifolds.

We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of variational cohomology to its classical is an isomorphism, provided that viewed as differential algebra, polynomials in finitely many variables. This theorem one key ingredients computation cohomology. For proof, we introduce sesquilinear Hochschild and Harrison complexes vanishing symmetric

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem o...