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# 24. Optimization

24.1 Linear Programming |  |
24.2 Quadratic Programming |  |
24.3 Nonlinear Programming |  |
24.4 Linear Least Squares |  |

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## 24.1 Linear Programming

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## 24.2 Quadratic Programming

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## 24.3 Nonlinear Programming

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## 24.4 Linear Least Squares

Function File: [beta, v, r] = gls (y, x, o)
  Generalized least squares estimation for the multivariate model with and , where is a by matrix, is a by matrix, is a by matrix, is a by matrix, and is a by matrix.

  Each row of y and x is an observation and each column a variable. The return values beta, v, and r are defined as follows.

  beta
    The GLS estimator for .

  v
    The GLS estimator for .

  r
    The matrix of GLS residuals, .

Function File: [beta, sigma, r] = ols (y, x)
  Ordinary least squares estimation for the multivariate model with and . where is a by matrix, is a by matrix, is a by matrix, and is a by matrix.

  Each row of y and x is an observation and each column a variable.

  The return values beta, sigma, and r are defined as follows.

  beta
    The OLS estimator for b, `beta = pinv (x) * y`, where `pinv (x)` denotes the pseudoinverse of x.

  sigma
    The OLS estimator for the matrix s,

        sigma = (y-x*beta)'
          * (y-x*beta)
          / (t-rank(x))

  r
    The matrix of OLS residuals, `r = y - x * beta`.

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This document was generated by John W. Eaton on March, 28 2005 using texi2html