Dual interior point algorithms

Abstract

For a linear programming problem stated in the canonical form we consider the dual problem and describe a class of interior point algorithms which generate monotonically improving approximations to its solution. We theoretically substantiate the optimization process in the admissible domain under the assumption that the dual problem is nondegenerate. In addition, we describe subsets of algorithms that lead to relative interior points of optimal solutions. These algorithms have linear and superlinear convergence rates. Moreover, we obtain a special subset of algorithms which generate iterative sequences of approximations to a solution of the direct problem, whose convergence rate exceeds that of the sequences of monotonically improving approximations to a solution of the dual problem.