Bound constraints

The nullspace_optimizer package includes the decorator bound_constraints_optimizable() for automating the implementation of bound constraints. It converts an optimization problem of the form

\[\begin{aligned} \min_{x\in \R^n}& \quad J(x)\\ \textrm{s.t.} & \left\{\begin{aligned} g_i(x)&=0, \text{ for all } 1\leqslant i\leqslant p,\\ h_j(x) &\leqslant 0, \text{ for all }1\leqslant j \leqslant q,\\ \end{aligned}\right. \end{aligned}\]

into

\[\begin{aligned} \min_{x\in \R^n}& \quad J(x)\\ \textrm{s.t.} & \left\{\begin{aligned} g_i(x)&=0, \text{ for all } 1\leqslant i\leqslant p,\\ h_j(x) &\leqslant 0, \text{ for all }1\leqslant j \leqslant q,\\ l& \leqslant x \leqslant u, \end{aligned}\right. \end{aligned}\]

where \(l\) and \(u\) are lower and upper bound vectors of dimension \(n\). The decorator is used as follows:

python

from nullspace_optimizer import EuclideanOptimizable, bound_constraints_optimizable

# Append the bound constraints l <= x <= u on the
# design variable x
@bound_constraints_optimizable(l,u)
class Problem(EuclideanOptimizable):
     def x0(self):
         #x0
     #...

     def J(self, x):
     # J

     # etc...

The decorator bound_constraints_optimizable() appends the bound constraints \(\texttt{l}\leqslant \texttt{x}\leqslant \texttt{u}\) to the optimization problem Problem, supposing that the design variable x, the lower bound l and the upper bound u are numpy arrays of the same size.

The design variable can also be a tuple of numpy array. See the full documentation of the decorator bound_constraints_optimizable().