Optimization problems with two-sided systems of linear equations over distributive lattices

Two-sided (max,min)-linear systems have applications in economics or in fuzzy set theory. A polynomial method for finding the maximum solution of a (max,min)-linear two-sided system has been recently proposed. The method is generalized in the paper to two-sided systems of linear equations over distributive lattices. Further, an iterative algorithm for the optimization problem given by a system of linear equations over a distributive lattice is described. The objective function of the problem is the maximum, or the minimum of several functions, all of which can be products of increasing, decreasing, or unimodular real functions. This general approach extends the possible range of applications.