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A Variable Step-Size Optimization Algorithm Based on a Special Numerical Method to Solve the System of Nonlinear Equations

After being studied the expression of figure-counting methods, a special numerical method is presented to approach any given value. With a gradual decrease weight of each digit, under the given error, any given data could be described by the permutation and combination of digits (-1, 0, 1). Based on this special numerical method, a new variable step-size optimization algorithm is designed to solve the system of nonlinear equations. According to the idea of this algorithm, the gradual decrease weight is considered as a variable step, and the change of each variable should be tested with the rule of ldquoForward, backward or maintain a steprdquo to approach the optimization objective, and the choice principle of the related variables has been discussed. The computer simulated results show that this algorithm can overcome the problems such as sensitivity to initial values, poor convergence reliability, and it is easy and practical to design.