Complete solution of a constrained tropical optimization problem with application to location analysis

摘要

We present a multidimensional optimization problem that is formulated andsolved in the tropical mathematics setting. The problem consists of minimizinga nonlinear objective function defined on vectors over an idempotent semifieldby means of a conjugate transposition operator, subject to constraints in theform of linear vector inequalities. A complete direct solution to the problemunder fairly general assumptions is given in a compact vector form suitable forboth further analysis and practical implementation. We apply the result tosolve a multidimensional minimax single facility location problem withChebyshev distance and with inequality constraints imposed on the feasiblelocation area.