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The purpose of this article is to give an overview of the theory of the and to show how to use it to define a on singular surfaces embedded in an (oriented) Euclidean space . In particular, we will introduce the notion of associated to a Borel subset of , generalizing the defined at each point of a smooth surface. For simplicity, we restrict our singular subsets to polyhedra of the -dimensional Euclidean space . The coherence of the theory lies in a convergence theorem: If a sequence of...
In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the
objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence...
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