USE OF CONTINUED ITERATION ON THE REDUCTION OF ITERATIONS OF THE INTERIOR POINT METHOD

ABSTRACT. Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the step which requires more processing time, and therefore, it should be done efficiently. The most common approach to solve them is the Cholesky factorization. However, Cholesky factorization demands a high computational effort in each iteration. Thus, searching for effort reduction, the continued iteration is proposed. This technique consists in determining a new direction through projection of the search direction and it was inserted into PCx code. The computational results regarding medium and large-scale problems, have indicated a good performance of the proposed approach in comparison with the predictor-corrector method

A variation on the interior point method for linear programming using the continued iteration

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOIn this paper, we present a proposal for a variation of the predictor-corrector interior point method with multiple centrality corrections. The new method uses the continued iteration to compute a new search direction for the predictor corrector method. The purpose of incorporating the continued iteration is to reduce the overall computational cost required to solve a linear programming problem. The computational results constitute evidence of the improvement obtained with the use of this technique combined with the interior point method.In this paper, we present a proposal for a variation of the predictor-corrector interior point method with multiple centrality corrections. The new method uses the continued iteration to compute a new search direction for the predictor corrector method. The purpose of incorporating the continued iteration is to reduce the overall computational cost required to solve a linear programming problem. The computational results constitute evidence of the improvement obtained with the use of this technique combined with the interior point method8516175CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãosem informação13th EUROPT Workshop on Advances in Continuous OptimizationJUL 08-10, 2015Edinburgh, SCOTLAN