1 Optimization

1.1 Quadratic Programming

qpsol

[x, obj, info, lambda]
   = qpsol (x, H, c, lb, ub, lb, A, ub)

Solve quadratic programs using Gill and Murray’s QPSOL. Because QPSOL is not freely redistributable, this function is only available if you have obtained your own copy of QPSOL. @xref{Installation}.

Tolerances and other options for qpsol may be specified using the function qpsol_options.

1.2 Nonlinear Programming

npsol

[x, obj, info, lambda]
   = npsol (x, 'phi', lb, ub, lb, A, ub, lb, 'g', ub)

Solve nonlinear programs using Gill and Murray’s NPSOL. Because NPSOL is not freely redistributable, this function is only available if you have obtained your own copy of NPSOL. @xref{Installation}.

The second argument is a string containing the name of the objective function to call. The objective function must be of the form

y = phi (x)

where x is a vector and y is a scalar.

Tolerances and other options for npsol may be specified using the function npsol_options.

1.3 Linear Least Squares

gls (Y, X, O)

Generalized least squares (GLS) estimation for the multivariate model

Y = X * B + E,  mean(E) = 0,  cov(vec(E)) = (s^2)*O

with

Y an T x p matrix
X an T x k matrix
B an k x p matrix
E an T x p matrix
O an Tp x Tp matrix

Each row of Y and X is an observation and each column a variable.

Returns BETA, v, and, R, where BETA is the GLS estimator for B, v is the GLS estimator for s^2, and R = Y - X*BETA is the matrix of GLS residuals.

ols (Y, X)

Ordinary Least Squares (OLS) estimation for the multivariate model

Y = X*B + E,  mean (E) = 0,  cov (vec (E)) = kron (S, I)

with

Y an T x p matrix
X an T x k matrix
B an k x p matrix
E an T x p matrix

Each row of Y and X is an observation and each column a variable.

Returns BETA, SIGMA, and R, where BETA is the OLS estimator for B, i.e.

BETA = pinv(X)*Y,

where pinv(X) denotes the pseudoinverse of X, SIGMA is the OLS estimator for the matrix S, i.e.

SIGMA = (Y - X*BETA)'*(Y - X*BETA) / (T - rank(X))

and R = Y - X*BETA is the matrix of OLS residuals.

About This Document

This document was generated on January 15, 2023 using texi2html 5.0.

The buttons in the navigation panels have the following meaning:

where the Example assumes that the current position is at Subsubsection One-Two-Three of a document of the following structure:

• 1. Section One
  • 1.1 Subsection One-One
    • ...
  • 1.2 Subsection One-Two
    • 1.2.1 Subsubsection One-Two-One
    • 1.2.2 Subsubsection One-Two-Two
    • 1.2.3 Subsubsection One-Two-Three     <== Current Position
    • 1.2.4 Subsubsection One-Two-Four
  • 1.3 Subsection One-Three
    • ...
  • 1.4 Subsection One-Four

This document was generated on January 15, 2023 using texi2html 5.0.