Logarithmic barrier constraint algorithm

Another constraint method is that of the logarithmic barrier algorithm. As in the Method of Multipliers this method is iterative. The function being minimised is replaced with

Φ(θ) = \begin{displaymath}\begin{cases}
\epsilon \sum_{i=1}^m -\log(b_i - A_i^T\theta)...
... \cdot \theta < b, \\ +\infty & \textrm{otherwise}. \end{cases}\end{displaymath} (14.19)

The value of ε is increased with each iteration, increase the logarithmic penalty. An advantage of this method over the Method of Multipliers is that gradients are not required.

The relax user manual (PDF), created 2016-10-28.