5.2 Iterated Sequential Baseline

Repeated handoffs are not automatically CCD¶

The conventional iterated sequential workflow alternates plant and control subproblems:

p^{k+1} = arg min_p J_p(p;z^k), z^{k+1} = arg min_z J_c(z;p^{k+1}).

Each discipline receives updated information, but the two subproblems retain different objectives, constraints, or approximations. Iteration can reduce handoff inconsistency, yet it does not create the single joint optimization problem required for CCD.

This distinction is important: iteration describes an algorithmic schedule; CCD describes a coupled system formulation. If block updates instead minimize the same $J_{sys}$ subject to all coupled constraints, the algorithm is a block-coordinate solver for CCD. That is not the conventional iterated baseline considered here.

Failure modes¶

Alternating discipline-specific optima can stall, oscillate, or converge to a point that is not stationary for the joint objective. A credible study reports the handoff residual

r_{handoff}^k = sqrt((p^{k+1}-p^k)^2 + (z^{k+1}-z^k)^2).

and then independently evaluates joint feasibility and system performance.

Activity 5.2: audit an iterated sequential baseline¶

Activity 5.2: audit an iterated sequential baseline

An alternating suspension workflow produces:

Cycle $k$	$k_s$ (kN/m)	gain $K$	$J_{sys}$	max normalized constraint
0	18.0	0.80	0.940	0.91
1	22.0	1.15	0.812	0.96
2	19.5	1.32	0.785	1.04
3	21.2	1.18	0.779	0.99
4	20.4	1.25	0.776	1.01

Use $r_k=sqrt{(k_s^k-k_s^{k-1})^2+(5(K^k-K^{k-1}))^2}$ and require $r_k≤0.5$ , maximum normalized constraint $≤1$ , and objective change no greater than 0.5 percent.

Compute $r_k$ for cycles 1–4.
Compute each percentage objective change.
Determine whether any cycle satisfies all three stopping requirements.
Quantify the constraint violation at cycle 4.
Explain why additional handoffs would not by themselves prove convergence to a CCD optimum.