Extra multistep BFGS updates in quasi-Newton methods

This note focuses on developing quasi-Newton methods that combine m+ 1 multistep and single-step updates on a single iteration for the sake of constructing the new approximation to the Hessian matrix to be used on the next iteration in computing the search direction. The approach considered here exploits the merits of the multistepmethods and those of El-Baali (1999) to create a hybrid technique. Our numerical results are encouraging and reveal that our proposed approach is promising. The newmethods compete well with El-Baali’s extra update algorithms (1999).