Overview of properties of different Hessian approximation schemes.

BFGS is the Broyden-Fletcher-Goldfarb-Shannon algorithm. SR1 is the Symmetric Rank-one update. GN is the Gauss-Newton approximation. SSM is the Structured Secant Method. TSSM is the Totally Structured Secant Method. FX is the hybrid method proposed by Fletcher and Xu [45]. GNSBFGS is the Gauss-Newton Structured BFGS method. The construction column indicates whether pointwise evaluation is possible or whether iterative construction is necessary. The positive semi-definite column indicates whether the approximation preserves positive semi-definiteness given a positive semi-definite initialization.