  The Piecewise Polynomial Interpolation (PPI) function approach is aimed at
solving nonlinear programming problems with disjoint feasible regions. In such
problems, disjointedness is generally associated with prohibited operating
zones, which correspond to bands of values that a variable is not allowed to
assume. An analytical implication of such prohibited operating zones is to make
the objective function, as well as its domain, discontinuous. The PPI function
approach consists in replacing the constraints associated with prohibited
operating zones by an equivalent set of equality and inequality constraints,
thereby allowing the application of any efficient gradient-based optimization
method for solving the equivalent problem. In this paper, we present the
definition of the PPI function and provide the mathematical proofs for its
properties.
