What are the characteristics of interior point penalty function method and exterior point penalty function method?

The characteristic of interior point penalty function method is that the exploration point is always kept in the feasible region when solving.

The characteristics of the exterior point penalty function method are: there is no requirement for the initial point, and any point in the definition domain can be taken at will.

Penalty function can be divided into exterior point method and interior point method, among which exterior point method is more general and can solve the problem that the constraint is a mixture of equality and inequality. Exterior point method has no requirement for initial point and can take any point in the definition domain at will. However, the initial point of the interior point method must be a point in the feasible region. When the constraint is complex, it is difficult to choose the initial point of the interior point method, and the interior point method can only solve the problem that the constraint is inequality.

Application of penalty function

1, motor optimization design

The application of generalized penalty function optimization method in motor optimization design not only avoids the optimization difficulty caused by improper acquisition of penalty factor in penalty function interior point method, but also retains the advantage of approaching the boundary. By adjusting the objective function and iterating the tolerance of the penalty function, the fast convergence can be achieved. At the same time, the generalized penalty function optimization method also has the characteristic of further searching for the best point near the boundary. In application, this method is a practical and effective interior point optimization method.

In the field of machinery, the computer optimization module compiled by generalized penalty function optimization method, combined with various exterior point methods or feasible scheme seeking methods, has remarkable optimization effect.

2. Generalized exponential factor prediction

The key to the realization of this model lies in the variable selection and coefficient estimation of the prediction equation. By introducing penalty function in the fitting process of linear regression model, the coefficient estimation of regression equation can be compressed, and the coefficients of some independent variables in the equation can be compressed to zero, so as to achieve the purpose of independent variable selection, reduce the error variance, ensure the stability of prediction equation, and thus improve the prediction accuracy. Therefore, it is reasonable to fit the generalized exponential factor prediction equation with penalty function method.