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In this work, we consider methods for large-scale and nonconvex unconstrainedoptimization. We propose a new trust-region method whose subproblem is definedusing a so-called "shape-changing" norm together with densely-initializedmultipoint symmetric secant (MSS) matrices to approximate the Hessian.Shape-changing norms and dense initializations have been successfully used inthe context of traditional quasi-Newton methods, but have yet to be explored inthe case of MSS methods. Numerical results suggest that trust-region methodsthat use densely-initialized MSS matrices together with shape-changing normsoutperform MSS with other trust-region methods.

Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices