An extended version of the memoryless DFP algorithm with the sufficient descent property

The classic memoryless DFP (Davidon–Fletcher–Powell) search direction is extended by embedding an additional term, as an uncomplicated scheme to obtain a strong sufficient descent property. Then, an improved memoryless DFP algorithm is given based on the Wolfe line search conditions, and its convergence is established. To provide support for the meaningfulness of our extension approach, some computational experiments have been conducted, mainly using the well-known CUTEr test problems and the Dolan–Moré criterion. The results confirm the well-functioning of the given algorithm.