Improved optimization algorithm by changing coordinate on the optimization problem with ridge

The reinforced wall interior point penalty function method and traditional exterior point penalty function method are both adopted to study the constrained optimization problem. Aim at the characteristics of the sequential unconstrained optimization problem with ridge, the improved algorithm for unconstrained optimization problem based on the changing coordinate is proposed, which is very suitable for the optimization method without calculating gradient, such as the coordinate transformation method, pattern searching method, and Powell´s method. The coordinate relation matrix is given and the computations of the examples are executed for the optimization problem with the equality and inequality constraints. The computing results show that the true optimum point is found by adopting the improved algorithm based on changing coordinate, otherwise the pseudo-optimum point is found. The one-dimensional blind-walking optimization method is also certified its validity. The reinforced wall interior point penalty method has no special requirement for the initial point, and then it has more applicability than the traditional internal point penalty method.