Is there a worked-out example of L-BFGS / L-BFGS-B?

In summary, L-BFGS and L-BFGS-B are optimization algorithms commonly used for solving large-scale nonlinear optimization problems. They use a quasi-Newton method to approximate the Hessian matrix and have efficient computation methods. L-BFGS / L-BFGS-B is different from other algorithms in its efficiency, convergence properties, and ability to handle box constraints. However, it may not perform well on problems with highly oscillatory or ill-conditioned Hessian matrices and requires the objective function to be continuous and differentiable. There are many resources and software packages available for working with L-BFGS / L-BFGS-B.
  • #1
chintanp
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I have seen the implementation of L-BFGS-B by authors in Fortran and ports in several languages. I am trying to implement the algorithm on my own.

I am having difficulty grasping a few steps. Is there a worked out example using L-BFGS or L-BFGS-B ? Something similar to http://www.cas.mcmaster.ca/~cs4te3/tutorials/BFGS.pdf explaining the output of each step in an iteration for a simple problem.
 
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  • #2
Try computer science forum
 

FAQ: Is there a worked-out example of L-BFGS / L-BFGS-B?

1. What is L-BFGS / L-BFGS-B?

L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) and L-BFGS-B (Limited-memory Broyden–Fletcher–Goldfarb–Shanno with box constraints) are optimization algorithms commonly used for solving large-scale nonlinear optimization problems.

2. How does L-BFGS / L-BFGS-B work?

L-BFGS / L-BFGS-B uses a quasi-Newton method to approximate the Hessian matrix of the objective function. It maintains a limited memory of previous iterations to efficiently compute the gradient and the Hessian-vector products, which are used to update the current iterate.

3. What makes L-BFGS / L-BFGS-B different from other optimization algorithms?

L-BFGS / L-BFGS-B is known for its efficiency in solving large-scale optimization problems, as it does not require the computation of the full Hessian matrix. It also has good convergence properties and can handle box constraints, making it a popular choice for many applications.

4. Are there any limitations to using L-BFGS / L-BFGS-B?

While L-BFGS / L-BFGS-B is generally efficient and effective, it may not perform well on problems with highly oscillatory or ill-conditioned Hessian matrices. It also requires the objective function to be continuous and differentiable.

5. Is there a worked-out example of L-BFGS / L-BFGS-B available?

Yes, there are many resources available online that provide step-by-step examples of using L-BFGS / L-BFGS-B for solving optimization problems. Additionally, many software packages, such as MATLAB and Python's SciPy library, have built-in functions for using L-BFGS / L-BFGS-B.

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