We consider a market with a certain number of agents and goods. Each agent has a position with respect to each good—either to receive it or to give it away. The objective is to construct an exchange plan that maximize the total value of the goods exchanged. In its discrete form, this problem can be formulated as a linear programming problem. However, solving it directly requires substantial computational resources. Therefore, we propose addressing a regularized version of the problem using an iterative algorithm.

The talk will focus on the structure of the solution to the regularized problem, how to obtain it, and why it converges to the solution of the original formulation.