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Problem solving

SECTION UNDER CONSTRUCTION.

Possible issues

  1. Modify sbound if isostaticity gap is negative for several steps due to abs(s_i)=sbound*R
  2. If isostaticity gap is too big (and positive), possibly there is small precision in the value of dual variables (e.g. when using Tulip). This could be solved by looking for dual variable larger than a given threshold value, but still needs to be implemented.
    1. This might be the case even when such gap is not too big. For instance, using GLPK in the LS tests, the initial iterations throw a gap of about +6 (due to very small forces)
  3. A negative isostaticity can be caused by the maximal displacement (of stable particles) being equal to the bound on $|s_{i,\mu}^\star|$. If this happens, try using a larger value of sbound.
    1. In reality, what happens is that there is an active dual variable related to such bound on the displacements and not to a contacts. Thus, the system is nonetheless isostatic, but a contact has not being properly counted, since it is not included in the lists of constraints in the main loop.
  4. The right convergence tolerance values, i.e. the right choice of tol_Γ_convergence and tol_S_convergence possibly depend on the solver
  5. Tulip.jl give an isostatic config only when the status of the optimization is ITERATION_LIMIT, which also entails that forces are determined with very, very low accuracy. Notably, even though this happens, the force mismatch is very small.

Setting the required precision

Overlaps occur

Due to numerical error

REAL overlaps

When this occurs, it is likely that the value of sbound is too large with respect of the value of $\ell$ used. So try using a larger value of ℓ0 (if this occurred when $\Gamma^\star$ was still relatively large).

Convergence not attained