On Mon Aug 24 Wang, Xue, Ph.D. Wang.Xue at mayo.edu wrote
> I am looking for a R version of Matlab function lsqlin. I came across
> R pracma package which has a lsqlin function. Compared with Matlab lsqlin,
> the R version does not allow inequality constraints.
> I am wondering if this functionality will be available in future. And also
> like to get your opinion on which R package/function is the best for
solving
> least square minimization problem with linear inequality constraints.
> Thanks very much for your time and attention!
Solving (linear) least-squares problems with linear inequality constraints
is more difficult then one would expect. Inspecting the MATLAB code reveals
that it employs advanced methods such as active-set (linear inequality
constraints) and interior-point (for bounds constraints).
Function nlsLM() in package *minpack.lm* supports bound constraints if that
is sufficient for you. The same is true for *nlmrt*. Convex optimization
might be a promising approach for linear inequality constraints, but there
is no easy-to-handle convex solver in R at this moment.
So the most straightforward way would be to use constrOptim(), that is
optim with linear constraints. It requires a reasonable starting point, and
keeping your fingers crossed that you are able to find such a point in the
interior of the feasible region.
I someone wants to try: Here is the example from the MATLAB "lsqlin" page:
C <- matrix(c(
0.9501, 0.7620, 0.6153, 0.4057,
0.2311, 0.4564, 0.7919, 0.9354,
0.6068, 0.0185, 0.9218, 0.9169,
0.4859, 0.8214, 0.7382, 0.4102,
0.8912, 0.4447, 0.1762, 0.8936), 5, 4, byrow=TRUE)
d <- c(0.0578, 0.3528, 0.8131, 0.0098, 0.1388)
A <- matrix(c(
0.2027, 0.2721, 0.7467, 0.4659,
0.1987, 0.1988, 0.4450, 0.4186,
0.6037, 0.0152, 0.9318, 0.8462), 3, 4, byrow=TRUE)
b <- c(0.5251, 0.2026, 0.6721)
The least-square function to be minimized is ||C x - d||_2 , and the
constraints are A x <= b :
f <- function(x) sum((C %*% x - d)^2)
The solution x0 returned by MATLAB has a minimum of f(x0) = 0.01759204 .
This point does not lie in the interior and cannot be used for a start.
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