A Method Identifying the Optimal Nonbasic Columns for the Problem Size Reduction in Affine Scaling Algorithm

애핀법에 있어서 문제 축소를 위한 최적비기저의 결정 방법

A modified primal-dual affine scaling algorithm for linear programming is presented. This modified algorithm generates an elipsoid containing all optimal dual solutions at each iteration, then checks whether or not a dual hyperplane intersects this ellipsoid. If the dual hyperplane has no intersection with this ellipsoid, its corresponding column must be optimal nonbasic. By condensing these columns, the size of LP problem can be reduced.