Simplicial algorithm to find zero points of a function with special structure on a simplotope

In this paper the authors introduce a variable dimension simplicial algorithm on a cartesian product of unit simplices to find a zero point of a continuous function with special structure. The special structure of the function allows the linear programming pivot steps of the algorithm to be performed in a small system of equations. Moreover, a special simplicial subdivision of the simplotope underlies the algorithm. The path of points generated by the algorithm approximately follows a piecewise smooth path in the simplotope. The latter path can be interpreted as being generated by an adjustment process. The authors discuss two applications, an international trade economy and an economy with increasing returns to scale. In both applications the zero points of the function induce equilibria in the economies.