R help - Aug 2015 - lsqlin in pracma

In solve.QP(), you don't need to expand the equality into two inequalities. 
It can DIRECTLY handle the equality constraints.  The first `meq' rows of
the constraint matrix are equality constraints. Here is the excerpt from  the
documentation.

meq
the first meq constraints are treated as equality constraints, all further as
inequality constraints (defaults to 0).


Therefore, solve.QP() can provide the full functionality of lsqlin in Matlab. 
However, one caveat is that the bounds constraints have to be implemented via
inequalities in solve.QP(), which is a slight pain, but not a deal breaker.

Best,
Ravi



	[[alternative HTML version deleted]]

> On 29 Aug 2015, at 18:29, Ravi Varadhan <ravi.varadhan at jhu.edu>
wrote:
> 
> In solve.QP(), you don't need to expand the equality into two
inequalities.  It can DIRECTLY handle the equality constraints.  The first
`meq' rows of the constraint matrix are equality constraints. Here is the
excerpt from  the documentation.
> 
> meq
> the first meq constraints are treated as equality constraints, all further
as inequality constraints (defaults to 0).
> 
> 
> Therefore, solve.QP() can provide the full functionality of lsqlin in
Matlab.  However, one caveat is that the bounds constraints have to be
implemented via inequalities in solve.QP(), which is a slight pain, but not a
deal breaker.
> 
It would be helpful if you could show us how to use solve.QP() in this case.
I?ve been trying with no success.

Berend

> On 29 Aug 2015, at 20:53, Berend Hasselman <bhh at xs4all.nl> wrote:
> 
> 
>> On 29 Aug 2015, at 18:29, Ravi Varadhan <ravi.varadhan at
jhu.edu> wrote:
>> 
>> In solve.QP(), you don't need to expand the equality into two
inequalities.  It can DIRECTLY handle the equality constraints.  The first
`meq' rows of the constraint matrix are equality constraints. Here is the
excerpt from  the documentation.
>> 
>> meq
>> the first meq constraints are treated as equality constraints, all
further as inequality constraints (defaults to 0).
>> 
>> 
>> Therefore, solve.QP() can provide the full functionality of lsqlin in
Matlab.  However, one caveat is that the bounds constraints have to be
implemented via inequalities in solve.QP(), which is a slight pain, but not a
deal breaker.
>> 
> 
> It would be helpful if you could show us how to use solve.QP() in this
case.
> I?ve been trying with no success.
> 
> B
I?ll answer my comment.

# Example from Matlab for lsqlin

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)

Dmat <- t(C) %*% C
dvec <- (t(C) %*% d)

Aeq <- c(3, 5, 7, 9)
beq <- 4
lb <- rep(-0.1, 4)   # lower and upper bounds
ub <- rep( 2.0, 4)

Amat <- rbind(Aeq,-A,diag(4),-diag(4))
bvec <- c(beq,-b,lb,-ub)
rslt <- solve.QP(Dmat, dvec, t(Amat), bvec, meq=1)
rslt$solution
sum(Aeq * rslt$solution) - beq
sum((C %*% rslt$solution - d)^2)


What a fiddle.

Berend