GENERALIZED HOMOGENEOUS AND SELF-DUAL ALGORITHM FOR LINEAR-PROGRAMMING

A generalized homogeneous and self-dual (HSD) infeasible-interior-point algorithm for linear programming (LP) is proposed in this paper. The algorithm does not need to start from a big M initial point, while achieving O((root n/beta(1-beta))L)-iteration complexity by following a certain central path on a central surface in a neighborhood N(beta), where beta can be any number between O and 1, n is the number of variables and L is the data length of the LP problem. In particular, an algorithm is developed, where the searching direction is obtained by solving a Newton equation system without infeasible residual terms on its right-hand side.