On the Well-posedness of Bayesian Inverse Problems

Well-posedness for Hyperbolic Problems

Tykhonov Well-Posedness for Quasi-Equilibrium Problems

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

Generic Well-posedness in Minimization Problems

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bound...

Well-posedness for Lexicographic Vector Equilibrium Problems

We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities.

Well-posedness of Inverse Problems for Systems with Time Dependent Parameters

In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by 〈ü(t), ψ〉V ∗,V + d(t; u̇(t), ψ) + a(t;u(t), ψ) = 〈f(t), ψ〉V ∗,V where V ⊂ VD ⊂ H ⊂ V ∗ D ⊂ V ∗ are Hilbert spaces with continuous and dense injections, where H is identified with its dual and 〈·, ·〉 denotes the associated duality product. We show under reasonable assumptions on the time-...