Updating quasi newton matrices with limited storage Sex chat petite

Under some suitable conditions, the global convergence property is established.The implementations of the method on a set of CUTE problems indicate that this extension is beneficial to the performance of the algorithm.

updating quasi newton matrices with limited storage-17

There are multiple published approaches using a history of updates to form this direction vector.

Here, we give a common approach, the so-called "two loop recursion." ensures that the search direction is well scaled and therefore the unit step length is accepted in most iterations.

Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm using a limited amount of computer memory.

It is a popular algorithm for parameter estimation in machine learning. Like the original BFGS, L-BFGS uses an estimation to the inverse Hessian matrix to steer its search through variable space, but where BFGS stores a dense n×n approximation to the inverse Hessian (n being the number of variables in the problem), L-BFGS stores only a few vectors that represent the approximation implicitly.

A Wolfe line search is used to ensure that the curvature condition is satisfied and the BFGS updating is stable.

Note that some software implementations use an Armijo backtracking line search, but cannot guarantee that the curvature condition Since BFGS (and hence L-BFGS) is designed to minimize smooth functions without constraints, the L-BFGS algorithm must be modified to handle functions that include non-differentiable components or constraints.

We then compare the L-BFGS method with the partitioned quasi-Newton method of Griewank and Toint (1982a).

The results show that, for some problems, the partitioned quasi-Newton method is clearly superior to the L-BFGS method.

Due to its resulting linear memory requirement, the L-BFGS method is particularly well suited for optimization problems with a large number of variables.

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