The problem of computing an equilibrium in an economy with constant returns to scale production technologies is to find prices and activity levels such that no activity makes positive profits and the market for each commodity is cleared. If one normalizes prices on the unit simplex, then this problem is equivalent to the so-called stationary point problem of the excess demand function in this economy on a particular subset of the unit simplex. This problem can be solved by approximating this stationary point problem by a sequence of linear stationary point problems. In this way one obtains an iterative algorithm. In each iteration of the sequence the linear stationary point problem is solved by an algorithm based on ideas of Kamiya and Talman.
Kremers, Johannes and Dolf Talman (1991), An SLSPP-algorithm to compute an equilibrium in an economy with linear production technologies, FEW Discussion Paper Series Discussion Paper FEW 496, Tilburg University, Tilburg, The Netherlands.