Sparsity exploitation in optimization

Does the fmincon algorithm exploit sparsity of hessians and jacobians while solving optimization problem ?

Answer 1

[SandeepKumar R]

A follow up question. Do they automatically detect sparsiy and switch to Large scale mode (sparsity exploited) or do we specifically have to supply some information to use this funtionality ?

[Alan Weiss]

Generally, the large-scale algorithms do the conversion to sparse linear algebra internally, and the medium-scale algorthms do the conversion to full linear algebra internally. I tried to state this in the link I gave ("Furthermore, you do not need to specify any sparse matrices to use a large-scale algorithm.").

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Alan Weiss]

There are several fmincon algorithms, and they each exploit sparsity differently. The term "large-scale" means that an algorithm exploits sparsity, as explained in Large-Scale vs. Medium-Scale Algorithms. A brief outline of the fmincon algorithms is given here, including which algorithms are large-scale.

Alan Weiss

MATLAB mathematical toolbox documentation