blf2: Bounded least squares

In PEIP: Geophysical Inverse Theory and Optimization

Bounded least squares

Description

Bounded least squares

Usage

blf2(A, b, c, delta, l, u)

Arguments

A	Design Matrix
b	Right hand side
c	matrix weight on x
delta	tolerance
l	lower bound
u	upper bound

Details

Solves the problem: min/max c'*x where || Ax-b || <= delta and l <= x <= u.

Value

x

solution

Author(s)

Jonathan M. Lees<[e-mail]>

References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

Stark, P.B. , and R. L. Parker, Bounded-Variable Least-Squares: An Algorithm and Applications, Computational Statistics 10:129-141, 1995.

Examples

###  set up an inverse problem:Shaw problem

n = 20
G = shawG(n,n)

spike = rep(0,n)
spike[10] = 1

spiken = G %*%  spike

wts = rep(1, n)
delta = 1e-03
set.seed(2015)
dspiken = spiken + 6e-6 *rnorm(length(spiken))

lb = spike - (.2) * wts
ub = spike + (.2) * wts

dspiken = dspiken

 blf2(G, dspiken, wts , delta, lb, ub)

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