SOLUTION OF ALGEBRAIC SYSTEMS OF DISJUNCTIVE EQUATIONS

This paper considers the solution of systems of equations that are exp ressed by the two sets: a global rectangular system of equations invol ving more variables than equations, and a set of conditional equations that are expressed as disjunctions. The set of disjunctions are given by equations and inequalities, where the latter define the domain of validity of the equations. In this way the solution of such a system i s defined by variables x satisfying the rectangular equations, and exa ctly one set of equations for each of the disjunctions. This paper foc uses mainly in the solution of systems of linear disjunctive equations . Using a convex hull representation of the disjunctions, the disjunct ive system of equations is converted into an MILP problem. A sufficien t condition is presented under which the model is shown to be solvable as an LP problem. The extension of the proposed method to nonlinear d isjunctive equations is also discussed. The application of the propose d algorithms are illustrated with several examples.