Interior-point Algorithm:
'interior-point' handles large, sparse problems, as well as small dense problems. The algorithm satisfies bounds at all iterations, and can recover from NaN or Inf results. It is a large-scale algorithm. The algorithm can use special techniques for large-scale problems.
Active-set Algorithm:
'active-set' can take large steps, which adds speed. The algorithm is effective on some problems with nonsmooth constraints. It is not a large-scale algorithm.
Large Scale vs Medium Scale Algorithms:
An optimization algorithm is large scale when it uses linear algebra that does not need to store, nor operate on, full matrices. This may be done internally by storing sparse matrices, and by using sparse linear algebra for computations whenever possible. Furthermore, the internal algorithms either preserve sparsity, such as a sparse Cholesky decomposition, or do not generate matrices, such as a conjugate gradient method.
In contrast, medium-scale methods internally create full matrices and use dense linear algebra. If a problem is sufficiently large, full matrices take up a significant amount of memory, and the dense linear algebra may require a long time to execute.
Please refer to the "Reasoning Behind the Recommendations" section on the link below:
