Abstract:
At every time step of the forward simulation of dense suspensions of rigid particles, a symmetric linear complementary problem (LCP) must be solved. Historically, approaches such as Baraff (active set) methods, interior point methods, and semi-smooth Newton methods have been used, but all of these methods become computationally infeasible when evaluating the matrix vector product (MVP) is expensive. This led to a reliance on simple proximal gradient methods to solve a non-negative quadratic program whose KKT conditions are equivalent to solving the LCP. These methods do not take advantage of the underlying structure. In our work, we leverage specialized proximal quasi-newton methods. Each MVP provides information about the underlying cost function restricted to a subspace. This motivates solving a subproblem to simultaneous optimization over multiple step sizes. Incomplete research is focused on multi-fidelity approaches motivated by access to faster inexact evaluations of the MVP.