An Augmented Lagrangian Method for Constrained Optimization Problems in Hilbert Spaces

Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds

This paper is devoted to the study of Newton-type algorithm for solving inclusions involving set-valued maps defined on Riemannian manifolds. We provide some sufficient conditions ensuring the existence as well as the quadratic convergence of Newton sequence. The material studied in this paper is based on Riemannian ge...

An Augmented Lagrangian Method for Reconstruction of the Robin Coefficients in Parabolic Equations

JOINT FORMULATION AND VARIATIONAL ANALYSIS OF OPTIMAL CONTROL WITH CUBIC POLYNOMIAL NONLINEARITY

In this article, we study an optimal control problem associated with  a nonlinear hyperbolic equation, including cubic polynomial nonlinearity and homogeneous Neumann conditions. Starting from an integral functional dependent on the initial data and the right-hand side of the equation, we establish the necessary condit...

Variational Problems with Pointwise Constraints on the Derivatives

This paper is concerned with the solvability of a class of nonlinear variational inequalities involving pointwise unilateral constraints on the laplacian. We describe the set of the pairs (ψ,h) of the right hand sides h and the obstacles ψ for which the problem has solutions and study the structure of the set of soluti...

Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space

In this paper, we research an anisotropic elliptic equation in the entire Euclidean space R^{N} . Under the assumption that the nonlinearity of the equation has exponential or critical growth, we prove, by means of the mountain-pass theorem, that the equation admits a nontrivial positive weak solution. Moreover, applyi...

Generic variational principles for supinf problems with constraints

We study supinf problems for perturbations of a given function of two variables by continuous bounded functions in the underlying spaces and the properties of the associated solution mapping. We provide conditions on the initial data such that most (in the Baire category sense) of the functions from the perturbation sp...