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

TL;DR

This paper introduces a novel parameter optimization approach for static equilibrium of discrete elastic rods, enhancing efficiency and robustness through an active-set Cholesky preconditioner and augmented Lagrangian splitting.

Contribution

It presents a new optimization framework that simultaneously tunes material and shape parameters under constraints, improving upon prior methods in speed and stability.

Findings

Outperforms previous methods in robustness and speed.

Ensures zero net force and physical law compliance.

Handles box constraints effectively.

Abstract

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 force 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 subproblem via simple vector updates. To efficiently solve the box-constrained primal subproblem, we propose a new active-set Cholesky preconditioner. Our method surpasses prior work in generality, robustness, and speed.