QPsolve failure case

[gilbo]

The following input to qpsolve:

Dmat:
[13,18,-6]
[18,27,-9]
[-6,-9,4]
dvec:
[-4,0,-100]
Amat:
[0]
[0]
[-1]
bvec:
[-25]

produces the solution vector:

[21:56:14.131] x:-3.999999999999967 y:-30.666666666666707 z:-100.00000000000006

which is incorrect as best I can ascertain. The problem above was arrived at by summing the energy

(2x + 3y - z)^2 + (x-4)^2 + (z-100)^2

with the additional constraint that

z <= 25

From that description it is clear that the answer should be x=4, z=25, and y set appropriately to zero out the first energy term

[cygnyx]

I see that quadprog has been updated.

[albertosantini]

Using the original quadprog package in R,

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> require(quadprog)
Loading required package: quadprog
> 
> Dmat <- matrix(c(13,18,-6, 18,27,-9, -6,-9,4),3,3)
> dvec <- c(-4,0,-100)
> Amat <- matrix(c(0,0,-1),3,1)
> bvec <- c(-25)
> 
> solve.QP(Dmat,dvec,Amat,bvec=bvec,meq=1)
$solution
[1] -4 11 25

$value
[1] 2804.5

$unconstrained.solution
[1]   -4.00000  -30.66667 -100.00000

$iterations
[1] 2 0

$Lagrangian
[1] 125

$iact
[1] 1

> Dmat
     [,1] [,2] [,3]
[1,]   13   18   -6
[2,]   18   27   -9
[3,]   -6   -9    4
> dvec
[1]   -4    0 -100
> Amat
     [,1]
[1,]    0
[2,]    0
[3,]   -1
> bvec
[1] -25
> 

With quadprog js

var dmat = [], dvec = [], amat = [], bvec = [], meq;

    dmat[1] = [];
    dmat[2] = [];
    dmat[3] = [];
    dmat[1][1] = 13;
    dmat[2][1] = 18;
    dmat[3][1] = -6;
    dmat[1][2] = 18;
    dmat[2][2] = 27;
    dmat[3][2] = -9;
    dmat[1][3] = -6;
    dmat[2][3] = -9;
    dmat[3][3] = 4;

    dvec[1] = -4;
    dvec[2] = 0;
    dvec[3] = -100;

    amat[1] = [];
    amat[2] = [];
    amat[3] = [];
    amat[1][1] = 0;
    amat[2][1] = 0;
    amat[3][1] = -1;

    bvec[1] = -25;

    meq = 1;

    qp.solveQP(dmat, dvec, amat, bvec, meq);

{ solution: [ , -4.000000000000016, 11.000000000000007, 25 ],
  Lagrangian: [ , 125 ],
  value: [ , 2804.500000000001 ],
  unconstrained_solution: [ , -3.999999999999967, -30.666666666666707, -100.00000000000006 ],
  iterations: [ , 2, 0 ],
  iact: [ , 1 ],
  message: '' }

The response seems quite similar apart numerical rounding.

Feel free to open an issue in https://github.com/albertosantini/node-quadprog/ project if you found cases where the figures between R package and js porting are different.