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# Optimization

## Quadratic Programming

## Nonlinear Programming

## Linear Least Squares

Function File: [beta, v, r] = gls (y, x, o)
  Generalized least squares estimation for the multivariate model where

  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 b.
  v
    The GLS estimator for `s^2`.
  r
    The matrix of GLS residuals, `r = y - x * beta`.

Function File: [beta, sigma, r] = ols (y, x)
  Ordinary least squares estimation for the multivariate model where

  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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