Well-posed variational formulations of Friedrichs-type systems

Well-posed Infinite Horizon Variational Problems

We give an effective sufficient condition for a variational problem with infinite horizon on a Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals’ flow in the cotangent bundle T ∗M ...

On Well-Posed Stochastic Formulations of Optical Flow

Well-posed fuzzy extensions of ill-posed linear equality systems

Linear equality systems with fuzzy parameters and crisp variables defined by the Zadeh’s extension principle are called possibilistic linear equality systems. This study focuses on the problem of stability (with respect to small changes in the membership function of fuzzy parameters) of the solution in these systems.

Well-posed Vector Optimization Problems and Vector Variational Inequalities

In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem generalizes the notion of well-setness for scalar optimization problems, introduced in [2]. On the other...

Reciprocals of well-posed linear systems

ear systems. Roughly speaking, these are generalizations of the finite-dimensional systems specified by 4 matrices A,B,C,D to systems with Hilbert spaces as the input, output and state spaces and unbounded generating operators A,B,C. The interest in this generalization is motivated by control and system theoretic problems for systems described by delay equations and partial differential equatio...