The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results

Bénichou, Michel; Gauthier, Jean-Michel; Hentges, Gerard; Ribière, Gerard

doi:10.1007/bf01584344

Cited by 144 publications

(32 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…where z is the ( m x 1) measurement mismatch vector and z is the ( n (12) where S, is an m x m diagonal matrix of row scales and S, an n x n diagonal matrix of column scales for the columns of H .…”

Section: W L a V Estimation U S I N G Scalingmentioning

confidence: 99%

See 1 more Smart Citation

Use of scaling in WLAV estimation of power system states

Çelik

Abur

1992

IEEE Trans. Power Syst.

View full text Add to dashboard Cite

Scaling has been widely used in linear programming problems for numerical stability and computational efficiency. This paper investigates the effectiveness of scaling in avoiding the leverage points in weighted least absolute value (WLAV) estimation of power system states. Existence of leverage points was claimed to be the reason for the WLAV estimator failing to reject bad data in the measurements. Simulation results indicate that scaling not only helps to reduce the leveraging effects but also improves the computational performance by decreasing the required number of Simplex iterations.

show abstract

Section: W L a V Estimation U S I N G Scalingmentioning

confidence: 99%

“…It involves the rowfcoluw scaling of the measurement Jacobian. Various scaling methods were suggested for the linear programming problems in the past [11,12]. However, no method has so far been singled out as the best for all applications.…”

Section: Introductionmentioning

confidence: 99%

Use of scaling in WLAV estimation of power system states

Çelik

Abur

1992

IEEE Trans. Power Syst.

View full text Add to dashboard Cite

show abstract

“…Once the perturbed problem has been solved, the perturbation is removed and the dual simplex algorithm is applied (often requiring no further iterations). If this approach were implemented with a perturbation of order ~c (rather than the much larger perturbation suggested in [3]), the solution to the perturbed problem could be accepted for all practical purposes.…”

Section: Resettingmentioning

confidence: 99%

A practical anti-cycling procedure for linearly constrained optimization

Gill

Murray

Saunders

et al. 1989

Mathematical Programming

113

View full text Add to dashboard Cite

A procedure is described for preventing cycling in active-set methods for linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance ofinfeasibilities in all variables, and maintenance of a "working" feasibility tolerance that increases over a long sequence of iterations. The additional work per iteration is nominal, and "stalling" cannot occur with exact arithmetic. The method appears to be reliable, based on computational results for the first 53 linear programming problems in the Netlib set.

show abstract

“…The BASIC procedure (sometimes known as INSsRr by uu5m, see Benichou et a., 1977) takes a set of variable names and values and produces a basic solution that has at least as good an objective value or sum of infeasibilities. The simplex method may then be applied to reach optimality.…”

Section: X-mentioning

confidence: 99%