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In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems....
In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...
In the paper, some sufficient optimality conditions for strict minima of order in constrained nonlinear mathematical programming problems involving (locally Lipschitz) -convex functions of order are presented. Furthermore, the concept of strict local minimizer of order is also used to state various duality results in the sense of Mond-Weir and in the sense of Wolfe for such nondifferentiable optimization problems.
We are concerned with two-level optimization problems called strongweak
Stackelberg problems, generalizing the class of Stackelberg problems in the
strong and weak sense. In order to handle the fact that the considered two-level
optimization problems may fail to have a solution under mild assumptions, we
consider a regularization involving ε-approximate optimal solutions in the lower
level problems. We prove the existence of optimal solutions for such regularized
problems and present some approximation...
In dimension one it is proved that the solution to a total variation-regularized
least-squares problem is always a function which is "constant almost everywhere" ,
provided that the data are in a certain sense outside the range of the operator
to be inverted. A similar, but weaker result is derived in dimension two.
In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand :
In this work we study the structure of approximate
solutions of autonomous variational problems with a lower
semicontinuous strictly convex integrand f : Rn×RnR1, where Rn is the n-dimensional Euclidean
space. We obtain a full...
We prove the periodicity of all H2-local minimizers with low energy
for a one-dimensional higher order variational problem.
The results extend and complement an earlier work of Stefan Müller
which concerns the structure of global minimizer.
The energy functional studied in this work is motivated by the
investigation of coherent solid phase transformations and the
competition between the
effects from regularization and formation of small scale structures.
With a special choice of a bilinear double...
We consider a static frictional contact between a nonlinear elastic body and a foundation. The contact is modelled by a normal compliance condition such that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element...
We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...
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