An interior point continuous path-following trajectory for linear programming

Abstract

In this paper, an interior point continuous path-following trajectory is proposed for linear programming. The descent direction in our continuous trajectory can be viewed as some combination of the affine scaling direction and the centering direction for linear programming. A key component in our interior point continuous path-following trajectory is an ordinary differential equation (ODE) system. Various properties including the convergence in the limit for the solution of this ODE system are analyzed and discussed in detail. Several illustrative examples are also provided to demonstrate the numerical behavior of this continuous trajectory.