A New and Efficient Interior Point Method Based on a Weight Vector for Solving LCCO Problems

Abstract

In this paper, we propose a new full-Newton step weighted interior point method for solving linearly constrained convex optimization problems (LCCO). This method is based on relaxing the complementarity condition using a non-negative variable weight vector to overcome the difficulty of finding an initial point in the neighborhood of central path required to start the classical interior point algorithms. With a zero of variable weight vector, the limit of the weighted path exists and satisfies the complementarity condition, this limit yields an optimal solution of LCCO problem. The advantage of this method is the use of a full-Newton step, which eliminates the step-size calculations with a quadratic rate of convergence. We study the complexity analysis of our method and derive a new iteration bound for small-update methods. Finally, some comparative numerical tests are stated to validate the effectiveness of our new method.