A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron , is globally asymptotically stable in . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.
The generalized linear differential equation where and the matrices are regular, can be transformed using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.
Let be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with and a control...
Let H be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [CITE]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with S and...