Finding an equilibrium in a linear exchange market model using modified barrier function

In this paper we describe an auctioning system that allows auction of goods and services in real time. For any given vector of goods and services and a set of consumers with vectors of preferences and budgets the system finds an equilibrium, i.e. such prices for each good and service that the total demand is equal to the given supply. The problem of finding the equilibrium is formulated as a special convex optimization problem. Application of the modified barrier function (MBF) method for solving such a problem leads to a pricing mechanism that allows finding the equilibrium in a timely manner. The system can be used for auctioning several goods and services for a number of consumers.