29,904 research outputs found
GMRES-Accelerated ADMM for Quadratic Objectives
We consider the sequence acceleration problem for the alternating direction
method-of-multipliers (ADMM) applied to a class of equality-constrained
problems with strongly convex quadratic objectives, which frequently arise as
the Newton subproblem of interior-point methods. Within this context, the ADMM
update equations are linear, the iterates are confined within a Krylov
subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its
ability to accelerate convergence. The basic ADMM method solves a
-conditioned problem in iterations. We give
theoretical justification and numerical evidence that the GMRES-accelerated
variant consistently solves the same problem in iterations
for an order-of-magnitude reduction in iterations, despite a worst-case bound
of iterations. The method is shown to be competitive against
standard preconditioned Krylov subspace methods for saddle-point problems. The
method is embedded within SeDuMi, a popular open-source solver for conic
optimization written in MATLAB, and used to solve many large-scale semidefinite
programs with error that decreases like , instead of ,
where is the iteration index.Comment: 31 pages, 7 figures. Accepted for publication in SIAM Journal on
Optimization (SIOPT
Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall
The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number
hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory
of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a
boundary has a significant influence on the swimmer’s trajectories and poses problems of dynamic
stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near
a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying
geometric structure of the dynamics, and establish a relation between the reversing symmetry of
the system and existence and stability of periodic and steady solutions of motion near the wall.
The results are demonstrated by numerical simulations and validated by motion experiments with
macroscale robotic swimmer prototypes
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