Optimizing Parameters for Static Equilibrium of Discrete Elastic Rods with Active-Set Cholesky

We propose a parameter optimization method for achieving static equilibrium of discrete elastic rods. Our method simultaneously optimizes material stiffness and rest shape parameters under box constraints to exactly enforce zero net forces while avoiding stability issues and violations of physical laws. For efficiency, we split our constrained optimization problem into primal and dual subproblems via the augmented Lagrangian method, while handling the dual maximization subproblem via simple vector updates. To efficiently solve the box-constrained primal minimization subproblem, we propose a new active-set Cholesky preconditioner for variants of conjugate gradient solvers with active sets. Our method surpasses prior work in generality, robustness, and speed.

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[Paper] (pdf, 17.5 MB)
[Supplementary Document] (pdf, 5.1 MB)
[Video] (mp4, 206 MB)
[arXiv]