Methods of Local Analysis

Abstract

In the local theory, we shall study the characterization and other properties of local best approximations. Local solutions will be determined to be global solutions only if this is possible by simple methods, i.e. without using topological methods. Specifically, we shall use results from the linear theory and from convex approximation, where the characterization of local solutions is performed via approximation on tangent sets. This involves replacing the nonlinear problem by a linearized one.