Complementarity Formulation for the Representation of Algebraic Systems Containing Conditional Equations

: Conditional models arise in chemical engineering when modeling systems involve physicochemical discontinuities, such as phase transitions. Zaher (1993) and Grossmann and Turkay (1996) show that one can represent conditional models as an algebraic system of disjunctive equations. This work proposes a new complementarity formulation for the representation of algebraic systems of disjunctive equations. This formulation not only establishes the complementarity condition among equations belonging to different disjunctive terms but also enforces simultaneous satisfaction of all of the equations in the same disjunctive term. This approach represents an alternative to MILP formulations, avoiding discrete decisions; it also avoids the need for special procedural nonlinear techniques as required by the boundary crossing algorithm (Zaher, 1991). We identify the disadvantages associated with the proposed formulation. Solving the resulting nonlinear system of equations relies on the assumption of..