# Questions tagged [quasi-newton]

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### Solution predictors for accelerating convergence in nonlinear FEM

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...
56 views

### Does BFGS preserve the bandedness of the inverse hessian?

In the BFGS method we perform iterations by calculating an approximation $\boldsymbol{H}_k$ to the inverse Hessian $\boldsymbol{H}$ of the objective function. This method belongs to a family of ...
116 views

### Sensitivity of BFGS to the accuracy of the gradient

I am studying how to speed-up the BFGS method using quantum computing techniques. I have used a method of speeding up the gradient of the function, but it sacrifices the precision value of the ...
88 views

### How to use Wolfe-Powell step-size control in quasi-Newton method?

I'm trying to find the minimum of a function using the quasi-Newton method with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. But I want to change the following implementation, so that: 1) ...
73 views

I'm trying to improve the speed of the following iteration to calculate $s_k$: $$B_k^{-1} = \Bigg( I + \frac{s_{k}s_{k-1}^T}{||s_{k-1}||^2}\Bigg)...\Bigg(I+ \frac{s_1s_0^T}{||s_0||^2}\Bigg) B_0^{-1}\\... 1answer 437 views ### Computational complexity of Newton's method the classical Newton's method for non-linear systems of equations is x_{k+1} =x_k-J_F(x_n)^{-1} F(x_n). In pratice, rather than compute the inverse of the Jacobian matrix, one solves the systems ... 0answers 225 views ### How to prevent BFGS from getting stuck on astronomically large gradient? I have implemented BFGS myself from scratch in order to solve minimization problems. Part of BFGS, as I understand it, is that the approximation to the Hessian is supposed to be positive definite, ... 1answer 402 views ### Linear constraints for L-BFGS-B I know L-BFGS-B only supports simple box constrains of the form: l_i \leq x_i \leq u_i, where l_i and u_i are constants. For my specific optimization problem, I need to specify some simple ... 0answers 85 views ### Minimize interesting objective function with knowledge of gradient nonlinearity? I plan on using a Quasi-Newton method (L-BFGS) to minimize a non-linear objective function.$$ f: \mathbb{R}^n \rightarrow \mathbb{R}$$The gradient is kind of interesting: as the values of the ... 0answers 233 views ### How to avoid the Broyden's jacobian approximation becoming poorer with the number of iterations? I have to solve many times a nonlinear system of the form$$f(x) = b^{(n)} inside a loop. The function $f$ is expensive to compute and I do not have its jacobian, so I have tried the good Broyden's ...
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I have read this and other threads on this site on BFGS, but I still don't have a clear understanding of what it's meant by low-rank updates. For example, I read the following in this book: The ...
62 views

### Doubt regarding principled approach towards approximating the Hessian

In my optimization problem, the hessian has a structure such that it can be written as the sum of two matrices. Populating the first of the matrices is efficient. Populating the second one is ...
131 views

### Quasi-Newton Optimization with parallel function evaluation

I have a function of many variables (~200-2000) which I am optimizing with some success using L-BFGS. While the function is expensive to evaluate, the gradient can be computed with not much additional ...
839 views

### Weighted Frobenius norm in BFGS

In what sense is the weighted Frobenius norm "adimensional"/"scale-invariant" for any symmetric positive definite weight matrix $W$? If we plug in a positive diagonal matrix into $W$ wee see that \$||A|...