  The aim of this paper is twofold: first, to extend the area of applications
of tropical optimization by solving new constrained location problems, and
second, to offer new closed-form solutions to general problems that are of
interest to location analysis. We consider a constrained minimax
single-facility location problem with addends on the plane with rectilinear
distance. The solution commences with the representation of the problem in a
standard form, and then in terms of tropical mathematics, as a constrained
optimization problem. We use a transformation technique, which can act as a
template to handle optimization problems in other application areas, and hence
is of independent interest. To solve the constrained optimization problem, we
apply methods and results of tropical optimization, which provide direct,
explicit solutions. The results obtained serve to derive new solutions of the
location problem, and of its special cases with reduced sets of constraints, in
a closed form, ready for practical implementation and immediate computation. As
illustrations, numerical solutions of example problems and their graphical
representation are given. We conclude with an application of the results to
optimal location of the central monitoring facility in an indoor video
surveillance system in a multi-floor building environment.
