[R] lsqlin in R package pracma

Raubertas, Richard
Thu, 27 Aug 2015 16:06:45 -0000

Is it really that complicated?  This looks like an ordinary quadratic
programming problem, and 'solve.QP' from the 'quadprog' package
seems to solve it without user-specified starting values:

library(quadprog)
Dmat <- t(C) %*% C
dvec <- (t(C) %*% d)
Amat <- -1 * t(A)
bvec <- -1 * b

rslt <- solve.QP(Dmat, dvec, Amat, bvec)
sum((C %*% rslt$solution - d)^2)

[1] 0.01758538

Richard Raubertas
Merck & Co.

-----Original Message-----
From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Hans W
Borchers
Sent: Wednesday, August 26, 2015 6:22 AM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] lsqlin in R package pracma

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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