Trajectory optimization of a mining dragline using the method of Lagrange multipliers

2010 ◽  
Vol 21 (14) ◽  
pp. 1677-1692
Author(s):  
C. H. McInnes ◽  
P. A. Meehan
Keyword(s):  
Lagrange Multipliers ◽  
Trajectory Optimization ◽  
Method Of Lagrange Multipliers

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

scholarly journals A generalization of Lagrange multipliers

1970 ◽  
Vol 3 (3) ◽  
pp. 353-362 ◽  
Author(s):  
B. D. Craven
Keyword(s):  
Banach Spaces ◽  
Lagrange Multipliers ◽  
Lagrange Equation ◽  
Linear Mapping ◽  
Real Field ◽  
Dimensional Problem ◽  
Continuous Linear ◽  
Continuous Linear Mapping ◽  
Finite Dimensional ◽  
Method Of Lagrange Multipliers

The method of Lagrange multipliers for solving a constrained stationary-value problem is generalized to allow the functions to take values in arbitrary Banach spaces (over the real field). The set of Lagrange multipliers in a finite-dimensional problem is shown to be replaced by a continuous linear mapping between the relevant Banach spaces. This theorem is applied to a calculus of variations problem, where the functional whose stationary value is sought and the constraint functional each take values in Banach spaces. Several generalizations of the Euler-Lagrange equation are obtained.

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