Convergence properties of minimization algorithms for convex constraints using a structured trust region

Abstract

In this paper, we present a class of trust region algorithms for minimization problems within convex feasible regions in which the structure of the problem is explicitly used in the definition of the trust region. This development is intended to reflect the possibility that some parts of the problem may be more accurately modelled than others, a common occurrence in large-scale nonlinear applications. After describing the structured trust region mechanism, we prove global convergence for all algorithms in our class.