Computational Methods for Finding Minimum Point of a Functional over a Manifold in Hilbert Space——Part 1. Restoration Operators and Approximate Curves of a Manifold

Abstract:

      In this paper, we first construct a class of restoration operators of a manifold in Hilbert space, anc discuss some properties of them. Secondly, the local parameter presentation of the manifold is built constructively by the restoration operators. This presentation will enable us to construct and implement the computational methods for finding minimum point of a functional over the manifold. Finally, this paper also constructs a class of approximate curves of the manifold, which providea a tool for obtaining implementoble algorithms. In these algorithms, we can apply the search along curvilinear paths rather than straight lines.