quadlin: Lagrange multiplier technique
In PEIP: Geophysical Inverse Theory and Optimization

quadlin

R Documentation

Lagrange multiplier technique

Description

Quadratic Linearization

Usage

quadlin(Q, A, b)

Arguments

`Q`	positive definite symmetric matrix
`A`	matrix with linearly independent rows
`b`	data vector

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.

Value

list:

`x`	vector of solution values
`lambda`	Lagrange multiplier

Author(s)

Jonathan M. Lees<jonathan.lees@unc.edu>

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 );

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.