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Questions tagged [quasi-newton]

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0answers
27 views

Inverse kinematics BFGS divergence

I am trying to implement inverse kinematics solver using BFGS as stated in the paper Xia2017. In the test experiment, i created 4 objects in 3-dimensional space: Node, Node1, Node2, Node3. Each Node ...
1
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1answer
53 views

Product of rank one updates as a low rank update for quasi newton/BFGS

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}\\...
3
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1answer
183 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 $...
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0answers
124 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, ...
4
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1answer
244 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 ...
5
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0answers
79 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 ...
4
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0answers
163 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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2answers
421 views

Low-rank updates in BFGS

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 ...
3
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1answer
59 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 ...
2
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0answers
109 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 ...
2
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0answers
591 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|...
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0answers
90 views

Quasi Newton taking very small steps

I have implemented a Quasi-Newton method based on the Hessian approximation. I am noticing that the algorithm takes too many iterations to converge, even though it does converge. What I am not able to ...
1
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1answer
95 views

The linear system in Quasi Newton method

I have implemented a Quasi Newton method for my problem, where I use the Hessian matrix approximation based approach. Hence, there is a linear system solve in every iteration. I solve the linear ...