A linear programming based algorithm to solve a class of optimization problems with a multi-linear objective function and affine constraints

We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems arises naturally in a number of settings in game theory, such as the bargaining problem, linear Fisher markets, and Kelly capacity allocation markets, but has applications in other fields of study as well. The algorithm computes an optimal solution when the number of variables in the multi-linear objective function is two, and an approximate solution when the number of variables is greater than two. A computational study demonstrates that when available computing time is limited the algorithm significantly outperforms well-known convex programming solvers IPOPT and CVXOPT, in terms of both efficiency and solution quality.