# Lagrange: Lagrange multipliers for LSE problem. In LSE: Constrained Least Squares and Generalized QR Factorization

## Description

Lagrange multipliers allows to give a analytic solution for equality constrained least squares problem (LSE).

## Usage

 `1` ```Lagrange(A,C,b,d) ```

## Arguments

 `A` Design matrix, m rows and n columns. `C` Constraint matrix, p rows and n columns. `b` Response vector for A, Ax=b, m rows and 1 column. `d` Response vector for C, Cx=d, p rows and 1 column.

## Details

The Lagrange multipliers method gives a numerical vector as the solution of a least squares problem (Ax=b) through unification the model and their restrictions in one function, the restrictions impose in the model (additional information, extramuestral information or a priori information) lead to another linear equality system (Cx=d). See significance constraint (x=0) or inclusion restriction (x+y=1), etc.

## Value

Numerical vector for a LSE problem.

## Author(s)

Sergio Andrés Cabrera Miranda Statician sergio05acm@gmail.com

## References

Rao, C. R., Toutenburg, H., Shalabh, H. C., & Schomaker, M. (2008). Linear models and generalizations. Least Squares and Alternatives (3rd edition) Springer, Berlin Heidelberg New York.

Theil, H. (1971). Principles of econometrics (No. 04; HB139, T44.).

## Examples

 ```1 2 3 4 5 6``` ```A = matrix(runif(50,-1,1),10,5) C = matrix(runif(20,-1,1),4,5) b = matrix(runif(10,-1,1),10,1) d = matrix(runif(4,-1,1),4,1) Lagrange(A,C,b,d) ```

LSE documentation built on Feb. 2, 2022, 5:07 p.m.