5.8 Convergence Behavior - Control Co-Design

Different workflows require different diagnostics¶

A one-pass baseline ends after its handoff; it has no joint convergence claim. An iterated sequential baseline can monitor handoff consistency, but a small handoff change does not imply stationarity of the joint system problem.

Nested CCD requires both a converged inner solution and a converged outer problem:

||r_{KKT,inner}|| ≤ ε_{in}, ||r_{KKT,outer}|| ≤ ε_{out}.

Simultaneous CCD uses the primal feasibility, complementarity, and stationarity residuals of the full sparse NLP. Both CCD formulations also require mesh and independent simulation checks.

Activity 5.8: decide which results have converged¶

Activity 5.8: decide which results have converged

Workflow	handoff change	inner KKT	outer/full KKT	max defect	max inequality
Iterated baseline	$3 × 10^{-4}$	—	—	$4 × 10^{-7}$	-0.006
Nested CCD	—	$7 × 10^{-7}$	$2 × 10^{-4}$	$5 × 10^{-7}$	-0.003
Simultaneous CCD	—	—	$8 × 10^{-6}$	$9 × 10^{-7}$	0.002

Use tolerances 10^-3 for handoff change, 10^-5 for KKT residuals, 10^-6 for defects, and 0 for inequalities.

Check every applicable criterion.
Identify which CCD result, if any, is numerically acceptable.
Quantify the simultaneous constraint violation.
Explain why the iterated baseline cannot claim CCD convergence despite its small handoff change.
Propose the next numerical action for each rejected CCD result.