On the optimal solution of the “saddle point problem”

On the optimal solution of the “saddle point problem”

The “saddle point problem” is of great interest because of its many applications in Science, Technology, Economics, etc. So, its effective solution is most imperative. In this talk the optimal solution is presented for the first time.
The “saddle point problem” is stated as follows:

“Determine a vector [x^T , y^T]^T ∈ ℝ^m+n , x ∈ ℝ^m , y ∈ ℝⁿ , n ≤ m satisfying the equation below

where Α ∈ ℝ^m×m is a nonsymmetric positive definite matrix, Β ∈ ℝ^m×n is rank deficient (rank(Β) = r < n), p ∈ ℝ ^m, q ∈ ℝ ⁿ and [p ^T , −q ^T ] ^T ∈ range(Α).”