About the Morse Theory for Certain Variational Problems.
Absolutely minimizing Lipschitz extensions on a metric space.
Abstract evolution equations on variable domains : an approach by minimizing movements
Abstract quasi-variational inequalities of elliptic type and applications
A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators...
Abstract Subdifferential Calculus and Semi-Convex Functions
∗ The work is partially supported by NSFR Grant No MM 409/94.We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function.
Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs
Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...
Abstract variational problems with volume constraints
Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.
Abstract variational problems with volume constraints
Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.
Active optimal control of the KdV equation using the variational iteration method.
Adherence of minimizers for dual convergences
Admissible functions in two-scale convergence.
Algebraic theory of discrete optimal control for multivariable systems [III.]
Algebraic theory of discrete optimal control for multivariable systems [II.]
Algebraic theory of discrete optimal control for multivariable systems [I.]
Algorithm for solving a generalized mixed equilibrium problem with perturbation in a Banach space.
Algorithmes de type F.A.C. en optimisation convexe
Algorithms construction for variational inequalities.
Algorithms for general mixed quasi variational inequalities.
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
Almost metric versions of Zhong's variational principle