Problem Instances

Standard Implementation

Problem instances in Taco are aimed at encapsulating the characteristics of the chance constrained problem to be solved. Such problems must store both the dataset of values of the random variable \(\xi\) as well as first-order oracles for the functions \(f\) and \(g\) involved.

Skeleton of such classes typically look that way:

class TypicalProblemInstance:

    def __init__(self, data):
        self.data = data

    # Two methods for the function value and gradient of the objective function, which depend only on the input x
    def objective_func(self, x):
        return 0.5 * np.dot(x,x)
    def objective_grad(self, x):
        return x

    # Two methods for the function value and gradient of the constraint function, which depend on both x and the random variable xi

    def objective_func(self, x, xi):
        return np.dot(x-xi, x-xi)
    def objective_grad(self, x, xi):
        return 2 * (x-xi)

In particular, the class must have a data attribute, which need to be a numpy array with 64-bit float precision and four methods to implement first order oracles for \(f\) and \(g\).

Numba compliant Implementation

Performances of the toolbox can be greatly improved when the user is able to provide a numba compliant class, i.e. implemented using the jitclass decorator.