A new quasi-Newton updating formula for sparse optimization calculations is presented. It makes combined use of a simple strategy for fixing symmetry and a Schubert correction to the upper triangle of a permuted Hessian approximation. Interesting properties of this new update are that it is closed form and that it does not satisfy the secant condition at every iteration of the calculations. Some numerical results are given that show that this update compares favorably with the sparse PSB update and appears to have a superlinear rate of convergence.

This new quasi-Newton update for sparse optimization calculations is closed form and shows a superlinear rate of convergence, compared to the sparse PSB update.

An Explicit Quasi-Newton Update for Sparse Optimization Calculations

Key Takeaway: This new quasi-Newton update for sparse optimization calculations is closed form and shows a superlinear rate of convergence, compared to the sparse PSB update.