SR1 Formula
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Symmetric Rank 1 (SR1) method is a quasi-Newton method to update the second derivative (Hessian) based on the derivatives (gradients) calculated at two points. It is a generalization to the secant method for a multidimensional problem. This update maintains the symmetry of the matrix but does not guarantee the update to be a positive definite matrix. For this reason it is the method of choice for indefinite problems. Given a function f(x), its gradient (nabla f),…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Symmetric Rank 1 (SR1) method is a quasi-Newton method to update the second derivative (Hessian) based on the derivatives (gradients) calculated at two points. It is a generalization to the secant method for a multidimensional problem. This update maintains the symmetry of the matrix but does not guarantee the update to be a positive definite matrix. For this reason it is the method of choice for indefinite problems. Given a function f(x), its gradient (nabla f), and Hessian matrix B, the Taylor series is: f(x_0+Delta x)=f(x_0)+nabla f(x_0)^T Delta x+frac{1}{2} Delta x^T {B} Delta x , and the Taylor series of the gradient itself: nabla f(x_0+Delta x)=nabla f(x_0)+B Delta x, is used to update B. Equation above (secant equation) can admit an infinite number of solutions to B.