We propose two positive parameters based on the choice of Birgin and Martínez search direction. Using the two classical choices of the Barzilai-Borwein parameters, two positive parameters were derived by minimizing the distance between the relative matrix corresponding to the propose search direction and the scaled memory-less Broyden–Fletcher–Goldfarb-Shanno (BFGS) matrix in the Frobenius norm. Moreover, the resulting direction is descent independent of any line search condition. We established the global convergence of the proposed algorithm under some appropriate assumptions. In addition, numerical experiments on some benchmark test problems are reported in order to show the efficiency of the proposed algorithm.
- derivative-free method
- nonlinear monotone operator equations
- self-scaling memory-less BFGS update