Luis F. Portugal

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In this paper, we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual(More)
Recently, Resende and Veiga [31] have proposed an e cient implementation of the Dual A ne (DA) interior-pointalgorithm for the solution of linear transportationmodels with integer costs and right-hand side coe cients. This procedure incorporates a Preconditioned Conjugate Gradient (PCG) method for solving the linear system that is required in each iteration(More)
ABSTRACT. We study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners are tested using PDNET, a state-of-the-art interior point code for the(More)
In this paper we discuss the use of block principal pivoting and predictor-corrector methods for the solution of large-scale linear least squares problems with nonnegative variables (NVLSQ). We also describe two implementations of these algorithms that are based on the normal equations and corrected seminormal equations (CSNE) approaches. We show that the(More)
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