A new algorithm for nonlinear L1-norm minimization with nonlinear equality constraints

Soliman, S. A.; Christensen, G. S.; Rouhi, Amir H.

doi:10.1016/0167-9473(91)90056-8

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…Actually they do not attack it directly, but mention it in passing, as having the same problems that they document for the methods of Soliman et al (1988Soliman et al ( , 1991 But if we apply Schlossmacher directly to their counterexamples, no problems occur. Our R code is presented below.…”

Section: Resultsmentioning

confidence: 99%

Simultaneous estimation of quantile curves using quantile sheets

Schnabel

Eilers

2012

AStA Adv Stat Anal

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The results of quantile smoothing often show crossing curves, in particular, for small data sets. We define a surface, called a quantile sheet, on the domain of the independent variable and the probability. Any desired quantile curve is obtained by evaluating the sheet for a fixed probability. This sheet is modeled by P-splines in form of tensor products of B-splines with difference penalties on the array of coefficients. The amount of smoothing is optimized by cross-validation. An application for reference growth curves for children is presented.

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Section: Resultsmentioning

confidence: 99%

Simultaneous estimation of quantile curves using quantile sheets

Schnabel

Eilers

2012

AStA Adv Stat Anal

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“…Hence J in (3) will always be the minimum value obtainable for the system under consideration, be it linear or nonlinear. As shown by computed examples in [5], we need to iterate in the nonlinear case in order to obtain the optimal solution. It is seen that the n equations thus chosen will bring the residuals in (3) to zero more quickly than any other choice of n equations.…”

Section: Contraction Mapping Theorem [14]mentioning

confidence: 99%

A new algorithm for finding the optimal solution of the least absolute value estimation problem

Christensen

Saif

Soliman

2007

Can. J. Electr. Comput. Eng.

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In this paper an algorithm is developed which uses contraction mapping to determine the optimal solution of the least absolute value (LAV) static estimation problem. It is noted that the new algorithm is computationally simpler than other methods currently available for this purpose. Minimal computational effort is required to obtain the LAV estimates.Dans cet article, on présente un algorithme développé qui utilise le traçage contracté pour déterminer la solution optimale du problème d'estimation statique de la moindre valeur absolue (LAV). On note que le nouvel algorithme est logistiquement plus simple que les autres méthodes actuellement disponibles dans ce but. Un minimum d'effort de calculs est requis pour obtenir les estimés de LAV. from 2000 to 2006, and as a Visiting Professor at Sultan Qaboos University, Muscat, during Fall 2006. He earned the first excellent medal and the incentive award as a best scientist in 1992. He has been chosen to be listed in the book Who's Who for the year 2007 for his achievements in his area of expertise. He has authored more than 110 refereed journal papers and more than 70 refereed conference papers. He has co-authored three books in his subject area. His research interests are in power quality, application of fuzzy systems to power systems, and application of state estimation to power systems.

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“…Later, due to claims that the introduced method does not generally guarantee the existence of a solution or the clear relationship between estimated values [12], the authors generalized the method for cases of repeated measurements and multi optimal solutions [13]. Eventually, the approach led to a new algorithm for nonlinear L 1 norm minimization problem with applications in power systems [8]. Hence, all of these LAV estimators partially employ Least Squares (LS) techniques in the estimation process.…”

Section: Motivationsmentioning

confidence: 99%

“…It can be considered to be a special case of WLS with equal weights. This method is usually used in power-system state estimation when the covariance matrix of measurements is unknown, or where it may lead to singularity of product matrices in the system of equations [8].…”

Section: Least Squares Estimatormentioning

confidence: 99%

“…Different estimators employ different techniques for obtaining the states. These techniques cover a wide range of methods: applying linear programming [37] and linear regression techniques [8], partial use of LS technique and weight matrix [30], employing residuals method [30], applying decoupled methods [28] or QR block decomposition method [23]. The method introduced in this research uses contraction mapping and singular value decomposition for state estimation.…”

Section: Literature Reviewmentioning

confidence: 99%

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