Abstract
The subject of this study is the analysis of the spectral secant equation for the well-known Davidon–Fletcher–Powell (DFP) quasi-Newton updating formula. More precisely, we plan to make the memoryless DFP formula well conditioned in several aspects. We first focus our efforts on obtaining eigenvalues of the DFP formula and directly analyzing its spectral condition number. Then, we proceed in a different direction by using the Byrd–Nocedal measure function as well. Lastly, we propose a hybrid adaptive formula for the spectral parameter of the method.