Solving minimal-optimal solutions for the generalized min-max programming problem with addition-min composition

Several forms of min-max programming problems with addition-min constraints have been introduced in the literature to model data transfer of BitTorrent-like peer-to-peer file-sharing systems. Solution algorithms are also provided to find the optimal solution which has equal values of all its variables. In this paper, we present a generalized min-max programming problem subject to addition-min constraints. A simple iterative approach is proposed to find the minimal-optimal solution for this generalized min-max programming problem. Numerical examples are provided to illustrate how the optimal solution with equal values for all its variables can be improved to become minimal-optimal.