The Improved Algorithm Of The Nonlinear Programming For Constrained Inequality Systems

On the based of the prompt development of theoretical studies on various optimization problems such as solving the linear programming, the nonlinear programming, the glossy programming, the non-smooth programming, the geometry programming, the integer programming, etc, this paper emphatically studys modified method of the nonlinear programming for constrained inequality systems. We consider the representative trust region method and the penalty function method which are chosed from inequality constrained optimization algorithms, and propose improved algorithm from the different view points.From now on, with the applicating of ABS algorithm, we add inequality equations to constrains and solve the nonlinear programming by combining ABS algorithm and the penalty function method. From the conclusions in the past, we find the improved algorithm is potential to a certain extent in the future. In this paper, we introduce the optimization theory and the development of inequality optimization, and improve two important methods, and we give their improved algorithm. We study the trust region method and the penalty function method that is used to solve the nonlinear programming for constrained inequality systems. The trust region method and the penalty function method are important numerical algorithms. To get improved algorithms, the trust region radius is changed by using nonmonotonic technology, we choose hyperbolic sine function as penalty factor and give numerical examples. ABS algorithm has been widely used in solving linear and nonlinear equations. We combine the ABS algorithm and penalty function method to solve the issue of increasing the conditions. The convergence of improved algorithms are proved.