Dear support team
As I?fd like to compare the different opimization criteria for the
muscle force distribution I?fm trying to understand the different
recruitment solver within AnyBody, most of all the two
variables ?elinear penalty?f and ?equadratic penalty?f. If I understood
it correctly the min/max solver minimizes the objective function
f(zi)= b + Qp * â€¡"zi,
where zi is the activity of muscle I, b is the maximum activity (with
zi<=b), and Lp is the linear penalty. In this case, when Lp = 0 the
maximum activity is minimized. When Lp is high, the sum of the muscle
activity will be minimized.
My question concerns the quadratic programming algorithm: what is
here the objective function to be minimized? Is it accordingly:
f(zi)= b + Qp * â€¡"zi^2?
If so, how high must Qp be that the minimization problem corresponds
to a minimization of the square sum of the muscle activity? I?fm
interested in the latter minimization. As the model consists of a lot
of muscle, at one point the quadratic programming solver doesn?ft find
a solution anymore (?eproblem is unbounded?f). When I decrease Qp (<35)
a solution is found. Now, I?fd like to know what this variable Qp
means. In a simple model (consisting of two segments connected by a
hinge joint, 2 agonistic and 1 antagonistic muscle, 1 external force)
it is easy to show that as Qp increases the solution converge to the
force distribution where the square sum of muscle activity is minimal
(as this simple problem is analytically solvable). But is it possible
to say how close to the latter solution I am with a smaller Qp?
By the way, have you changed the quadratic programming solver in the
beta version 2.0? Strangely, in the new version the problem is always
unbounded using the OOSOLQP recruitment solver, although it is
exactly the same model, which worked quite well in the old version.
Thanks a lot for your help