Source code for PEPit.functions.convex_function

from PEPit.function import Function


[docs]class ConvexFunction(Function): """ The :class:`ConvexFunction` class overwrites the `add_class_constraints` method of :class:`Function`, implementing the interpolation constraints of the class of convex, closed and proper (CCP) functions (i.e., convex functions whose epigraphs are non-empty closed sets). General CCP functions are not characterized by any parameter, hence can be instantiated as Example: >>> from PEPit import PEP >>> from PEPit.functions import ConvexFunction >>> problem = PEP() >>> func = problem.declare_function(function_class=ConvexFunction) """ def __init__(self, is_leaf=True, decomposition_dict=None, reuse_gradient=False): """ Args: is_leaf (bool): True if self is defined from scratch. False if self is defined as linear combination of leaf. decomposition_dict (dict): Decomposition of self as linear combination of leaf :class:`Function` objects. Keys are :class:`Function` objects and values are their associated coefficients. reuse_gradient (bool): If True, the same subgradient is returned when one requires it several times on the same :class:`Point`. If False, a new subgradient is computed each time one is required. """ super().__init__(is_leaf=is_leaf, decomposition_dict=decomposition_dict, reuse_gradient=reuse_gradient)
[docs] def add_class_constraints(self): """ Formulates the list of interpolation constraints for self (CCP function). """ for point_i in self.list_of_points: xi, gi, fi = point_i for point_j in self.list_of_points: xj, gj, fj = point_j if point_i != point_j: # Interpolation conditions of convex functions class self.list_of_class_constraints.append(fi - fj >= gj * (xi - xj))