20.9 Distributed and Networked CCD

Core idea¶

Distributed and Networked CCD must be treated as a system-level decision rather than an isolated technique. For a reproducible repository with versioned models, data, formulations, solvers, tests, results, and hardware evidence, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are interfaces, design and trajectory data, derivatives, metadata, seeds, tolerances, and provenance. The chapter-level formulation is

\mathrm{reproducibility}=\mathrm{model}+\mathrm{data}+\mathrm{configuration}+\mathrm{environment}+\mathrm{evidence}.

For this section, trace how the choice changes system synthesis, the active constraints, and the implementable engineering design. A method is useful only when its assumptions are explicit and its result answers the same system question as the baseline.

Engineering interpretation¶

Ask three questions:

Which physical, informational, computational, or economic resource changed?
Which objective component or active constraint made the change valuable?
Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to reproduce evidence. Record units and assumptions before optimization, report component objectives and margins afterward, and verify the result using an independent calculation or higher-fidelity model.

Activity 20.9: audit distributed convergence¶

Activity 20.9: audit distributed convergence

Six subsystem agents solve a consensus CCD problem with ADMM. The primal residual $r_k$ , dual residual $s_k$ , and distributed objective are recorded below; the centralized reference objective is 12.40.

Iteration $k$	$r_k$	$s_k$	Objective
0	1.80	1.20	15.80
5	0.42	0.31	13.05
10	0.105	0.082	12.58
20	0.0090	0.0120	12.43
40	0.0007	0.0011	12.405

Convergence requires $r_k,s_k\leq0.01$ and objective error below 0.5%.

Compute relative objective error at every recorded iteration and identify the first accepted iterate.
Estimate average geometric contraction factors for $r_k$ over iterations 5–10 and 20–40.
Each agent sends 24 double-precision values to two neighbors per iteration. Compute total transmitted bytes through the accepted iteration, excluding protocol overhead.
Local computation takes 45 ms per iteration and communication adds 8 ms normally. Estimate wall time. Repeat for a degraded network with 35 ms communication latency.
One agent uses an outdated model and converges to objective 12.31 with residuals below tolerance. Quantify the apparent improvement and explain why residual convergence cannot replace model-version provenance.