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In this paper the development, and numerical testing of a class of self-scaling Quasi-Newton update with adaptive step - size are presented . In our work a new combined (Oren-Al-Bayati) self-scaling algorithm is presented with a modified Armijo line search procedure. This algorithm has implemented both theoretically and numerically and tested on some well-known test cases. Numerical experiments indicate that this new algorithm is effective and superior to the standard, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).

New Hybrid (Oren- Al-Bayati) Self-Scaling Algorithm With Armijo Line-Search