The compute of Hessian may be wrong

[ZzhengP]

orca/src/math/WeightedEuclidianNormFunction.cc

Line 43 in 39fe1f4

Hessian_.noalias() = SelectionVector.asDiagonal() * Weight * A.transpose() * A ;

In orca, the Hessian matrix of qpOASES is computed like , the first term is the weight.
For qpOASES, the problem is formulated like
.
Finally, we have to multiply the Hessian matrix computed in ORCA by 2 for qpOASES.

[rlober]

The 1/2 won't affect the global optimum as long as it is missing (or present) for all objectives.

[ZzhengP]

When I define a class of gravity regularization, I define E like a identity matrix and f equals to -g. But the simulation shows that the robot compensates too much gravity torque. By multiplying H by 2, I solved the problem. I think 1/2 affect regularization resolution.

[rlober]

It still shouldn't make any difference because the gradient is multiplied by 2 already :

orca/src/math/WeightedEuclidianNormFunction.cc

Line 51 in 39fe1f4

Gradient_.noalias() = 2.0 * SelectionVector.asDiagonal() * Weight * A.transpose() * b ;

0.5 x'Hx +x'g = x'Hx + 2x'g

Can you post links to the relevant parts of your code? I think the problem is something more subtle.

[ZzhengP]

(Ex+f)'(Ex+f) = (x'E'Ex + 2x'E'f) = x'Hx + x'g. Therefore, this factor 2 means 2E'f = g.
https://github.com/ZzhengP/Stage_M2/blob/b4b9c2b77ed5880b013df82be87038c462ffcbb6/rtt_orca_reg.hpp#L13

[ahoarau]

(Ex+f)'(Ex+f) = (x'E'Ex + 2x'E'f)
and
0.5 x'Hx +x'g = x'Hx + 2x'g

Means that
H = E'E
and
E'f = g

In the code it's 2E'f = g

Problem ! Thanks for reporting. This is a nasty one

[ahoarau]

Fixed in 64f5637
Thanks !