Finding all solutions of piecewise-linear equations using linear programming

A linear programming(LP) algorithm was developed to more efficiently find all solutions of piecewise-linear equations than the traditional LP algorithm.This algorithm first finds the hypercube consisting of the various linear regions with the equations being other convex or concave in this hypercube.Then,specific LP problems are solved in the hypercube to determine whether the solution exists.For the example given in this paper,the algorithm uses only 25% as many linear programs as the conventional LP algorithm.Thus this algorithm is more efficient than the conventional LP algorithm since it reduces the number of linear programs that need to be solved.The improved performance compared to the conventional LP algorithm depends on the equation properties.