Add bounds to BHHH

docs/source/algorithms.md

@@ -578,25 +578,34 @@ We implement a few algorithms from scratch. They are currently considered experi
 
         "bhhh"
 
-    Minimize a likelihood function using the BHHH algorithm.
+    Minimize a likelihood function using the box-constraint BHHH algorithm.
 
     BHHH (:cite:`Berndt1974`) can - and should ONLY - be used for minimizing
-    (or maximizing) a likelihood. It is similar to the Newton-Raphson
+    (or maximizing) a likelihood function. It is similar to the Newton-Raphson
     algorithm, but replaces the Hessian matrix with the outer product of the
     gradient. This approximation is based on the information matrix equality
     (:cite:`Halbert1982`) and is thus only vaid when minimizing (or maximizing)
     a likelihood.
 
+    Bounds, i.e. box constraints, are supported. In order to identify the active
+    constraints in the set of inequality constraints, an epsilon-active-set approach is
+    used (see, e.g. :cite:`Nocedal2006`, p. 308, for the active-set method in general and
+    :cite:`Kelley1999`, p. 97, on the estimation of epsilon-active sets a la the
+    Projected BFGS–Armijo algorithm).
+
     The criterion function :func:`func` should return a dictionary with
     at least the entry ``{"contributions": array_or_pytree}`` where ``array_or_pytree``
     contains the likelihood contributions of each individual.
 
     bhhh supports the following options:
 
-    - **convergence_absolute_gradient_tolerance** (float): Stopping criterion for the
-      gradient tolerance. Default is 1e-8.
-    - **stopping_max_iterations** (int): Maximum number of iterations.
-      If reached, terminate. Default is 200.
+    - **convergence.relative_params_tolerance** (float): Stop when the relative movement
+            between parameter vectors is smaller than this. The default is 1e-8.
+    - **convergence.absolute_gradient_tolerance** (float): Stop if all elements of the
+            projected gradient are smaller than this. The default is 1e-8.
+    - **stopping.max_iterations** (int): If the maximum number of iterations is reached,
+      the optimization stops, but we do not count this as convergence.
+      The default is 200.
 
 ```
 

docs/source/refs.bib

@@ -884,4 +884,13 @@ @article{Zhang2010
 URL = {https://doi.org/10.1137/09075531X},
 }
 
+@book{Kelley1999,
+author = {Kelley, C. T.},
+title = {Iterative Methods for Optimization},
+publisher = {Society for Industrial and Applied Mathematics},
+year = {1999},
+doi = {10.1137/1.9781611970920},
+URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970920},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}