Gradient mappings

Gradient Mappings

Averaged Mappings and the Gradient-Projection Algorithm

It is well known that the gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this article, we first provide an alternative averaged mapping approach to the GPA. This approach is operator-oriented in nature. Since, in general, in infinite-dimensional Hilbert spaces, GPA has only weak convergence, we provide two modifications of GPA...

Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition

This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behav...

A Hybrid Gradient-Projection Algorithm for Averaged Mappings in Hilbert Spaces

It is well known that the gradient-projection algorithm GPA is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrain...

Deriving Concept Mappings through Instance Mappings

Ontology matching is a promising step towards the solution to the interoperability problem of the Semantic Web. Instance-based methods have the advantage of focusing on the most active parts of the ontologies and reflect concept semantics as they are actually being used. Previous instance-based mapping techniques were only applicable to cases where a substantial set of instances shared by both ...