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 vector is used in the stopping criteria of the iterative solver employed for the solution of the system. In the implementation, a preconditioned conjugate gradient method is used as the iterative solver. The details of the implementation are described and the code PDNET is tested on a large set of standard minimum‐cost network flow test problems. Computational results indicate that the implementation is competitive with state‐of‐the‐art network flow codes. © 2000 John Wiley & Sons, Inc.

Abstract. 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 method of normal equations should be employed in the implementation of the predictor-corrector algorithm. This type of approach should also be used in the implementation of the block principal pivoting method, but a switch to the CSNE method may be useful in the last iterations of the algorithm. Computational experience is also included in this paper and shows that both the predictor-corrector and the block principal pivoting algorithms are quite efficient to deal with large-scale NVLSQ problems.

Recently, Resende and Veiga [SIAM J. Optim., 3 (1993), pp. proposed an efficient implementation of the dual affine (DA) interior-point algorithm for the solution of linear transportation models with integer costs and fight-hand-side coefficients. This procedure incorporates a preconditioned conjugate gradient (PCG) method for solving the linear system that is required in each iteration of the DA algorithm. In this paper, we introduce an incomplete Q R decomposition (IQRD) preconditioning for the PCG algorithm. Computational experience shows that the IQRD preconditioning is appropriate in this instance and is more efficient than the preconditioning introduced by Resende and Veiga. We also show that the primal dual (PD) and the predictor corrector (PC) interior-point algorithms can also be implemented by using the same type of technique. A comparison among these three algorithms is included and indicates that the PD and PC algorithms are more appropriate for the solution of transportation problems with well-scaled cost and right-hand-side coefficients and assignment problems with poorly scaled cost coefficients. On the other hand, the DA algorithm seems to be more efficient for assignment problems with well-scaled cost coefficients and transportation problems whose cost coefficients are badly scaled.

We describe Fortran subroutines for network flow optimization using an interior point network flow algorithm, that, together with a Fortran language driver, make up PDNET. The algorithm is described in detail and its implementation is outlined. Usage of the package is described and some computational experiments are reported. Source code for the software can be downloaded at http://www.research.att.com/~mgcr/pdnet.

This paper presents an aerial-ground field robotic team, designed to collect and transport soil and biota samples in estuarine mudflats. The robotic system has been devised so that its sampling and storage capabilities are suited for radionuclides and heavy metals environmental monitoring. Automating these time-consuming and physically demanding tasks is expected to positively impact both their scope and frequency. The success of an environmental monitoring study heavily depends on the statistical significance and accuracy of the sampling procedures, which most often require frequent human intervention. The bird's-eye view provided by the aerial vehicle aims at supporting remote mission specification and execution monitoring. This paper also proposes a preliminary experimental protocol tailored to exploit the capabilities o↵ered by the robotic system. Preliminary field trials in real estuarine mudflats show the ability of the robotic system to successfully extract and transport soil samples for o✏ine analysis.