Symbolic differentiation

The nullspace_optimizer package includes the decorator symbolic_optimizable() that enables to implement optimization programs with symbolic objective and constraint functions.

For instance, the optimization problem

\[\newcommand{\<}{\leq} \begin{aligned} \min_{(x_0,x_1)\in\mathbb{R}^2} & \quad x_1+0.3 x_0 \\ s.t. &\quad \left\{ \begin{aligned} -x_1+\frac{1}{x_0} & \< 0\\ -(3-x_0-x_1) & \< 0 \end{aligned}\right. \end{aligned}\]

can be implemented symbolically as follows:

python

from nullspace_optimizer import EuclideanOptimizable, symbolic_optimizable

@symbolic_optimizable
class basicProblem(EuclideanOptimizable):
    def x0(self):
        return [1.5, 2.25]

    def J(self, x):
        return x[1]+0.3*x[0]

    def H(self, x):
        return [-x[1]+1.0/x[0], -(3-x[0]-x[1])]

Only the objective and constraint functions need to be specified, their derivatives being obtained with Sympy symbolic differentiation. The decorator symbolic_optimizable() is compatible with the use of arbitrary Sympy symbolic operators.