PEIP (version 2.2-5)

quadlin: Lagrange multiplier technique

Description

Quadratic Linearization

Usage

quadlin(Q, A, b)

Value

list:

x

vector of solution values

lambda

Lagrange multiplier

Arguments

Q

positive definite symmetric matrix

A

matrix with linearly independent rows

b

data vector

Author

Jonathan M. Lees<[e-mail]>

Details

Solves the problem: min (1/2) t(x)*Q*x with Ax = b. using the Lagrange multiplier technique, where Q is assumed to be symmetric and positive definite and the rows of A are linearly independent.

Examples

###%    Radius of the Earth (km)
    Re=6370.8;
rad = 5000
ri=rad/Re;

q=c(1.083221147,  1.757951474)
H = matrix(rep(0, 4), ncol=2, nrow=2)

H[1,1]=1.508616069 - 3.520104161*ri + 2.112062496*ri^2;
H[1,2]=3.173750352 - 7.140938293*ri + 4.080536168*ri^2;
H[2,1]=H[1,2];
H[2,2]=7.023621326 - 15.45196692*ri + 8.584426066*ri^2;
A1 =quadlin(H,t(q), 1.0 );