A bornological approach to rotundity and smoothness applied to approximation.
A generalization of Dubovitskij-Miliutin theorem
A generalization of Ekeland's variational principle with applications.
A generalized solution of a nonconvex minimization problem and its stability
A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces.
A Lagrange multiplier theorem and a sandwich theorem for convex relations.
A Landesman-Lazer alternative theorem for a class of optimization problems.
A note on approximate solutions in parametric semi-infinite optimization
A relaxation theorem for partially observed stochastic control on Hilbert space
In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that...
A Remark on Variational Principles of Choban, Kenderov and Revalski
We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.
A Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza locale della soluzione di una equazione di Riccati che si incontra in un problema di controllo ottimale. In ipotesi di regolarità per il costo si prova resistenza globale. Il problema astratto considerato è il modello di alcuni problemi di controllo ottimale governati da equazioni paraboliche con controllo sulla frontiera.
Abstract evolution equations on variable domains : an approach by minimizing movements
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.
Algorithm for solving a generalized mixed equilibrium problem with perturbation in a Banach space.
Algorithmes de type F.A.C. en optimisation convexe
An active set strategy based on the augmented lagrangian formulation for image restoration
An active set strategy based on the augmented Lagrangian formulation for image restoration
Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...
An asymptotical variational principle associated with the steepest descent method for a convex function.
An Existence Theorem for Class of Non-Coercive Optimization and Variational Problems.