Finding an initial solution and modifying search direction by the centering force in the primal-dual interior point method

원쌍대 내부점기법에서 초기해 선정과 중심화 힘을 이용한 개선 방향의 수정

This paper deals with finding an initial solution and modifying search direction by the centrering force in the predictor-corrector method which is a variant of the primal-dual barrier method. These methods were tested with NETLIB problems. Initial solutions which are located close to the center of the feasible set lower the number of iterations, as they enlarge the step length. Three heuristic methods to find such initial solution are suggested. The new methods reduce the average number of iterations by 52% to at most, compared with the old method assigning 1 to initial valurs. Solutions can move closer to the central path fast by enlarging the centering force in early steps. It enlarge the step length, so reduces the number of iterations. The more effective this method is the closer the initial solution is to the boundary of the feasible set.