Numerical algorithm: The conjugate direction method of multi-dimensional optimization without constrained optimization

In efficiency, the conjugate direction method is located between the steepest descent method and the Newton method. It has characteristics: for n-dimensional two-type problems, the results can be obtained in N-step, the conjugate gradient method does not need to calculate the Haisen matrix;

Conjugate direction:

Q is the n-order real symmetric matrix, for direction D (0), D (1),..., D (M), if for all I is not equal to J, there is D (i) TQd (j) = 0, it is said that they are about Q conjugate.

theorem: If q is an n-order positive definite matrix (naturally symmetrical), if the direction d (0), D (1),..., D (k), k<=n-1 nonzero, and is about Q conjugate, then they are linearly independent;

n conjugate vector method for constructing n-order positive definite matrices: Gram-schmidt

1, the basic conjugate direction algorithm

Numerical algorithm: The conjugate direction method of multi-dimensional optimization without constrained optimization