I frequently encounter cases, such as the ones below, where you seemingly have two hyphenated compound adjectives modifying a noun. I know that in such cases that you should join the compound adjectives with an en dash.
However, in case (1) the author later wrote "…dual-hop MARNs…", using the initialism to denote the noun; thus, illustrating that "Multiple-access" is not a hyphenated compound adjective. Hence, my problem is what should be done in case (1). Should the noun be hyphenated right the way through to show that it is indeed one unit, as in "Dual-Hop Multiple-Access-Relay-Networks", or is their another way?
(1) Dual-Hop Multiple-Access Relay Networks
(2) Semi-definite Programming-based Approach
If you write (1) as "Dual-Hop(en dash)Multiple-Access Relay Networks, then I think this implies that "dual-hop relay networks" exist and that "multiple-access relay networks" exist independently of each other, which may not actually be the case.
Please help me out here because these things crop up so often in my work.
Best Answer
You seem to be misunderstanding how compound adjectives and en dashes work.
As you yourself quoted, the Chicago Manual of Style says:
This does not mean what you state in your first paragraph:
It is not the case that you should join two hyphenated compound adjectives modifying a noun with an en dash, or with anything else for that matter. Two separate adjectives (whether compound or hyphenated or not) should never be joined by anything—that’s why they’re separate.
(For our present purposes, I will simply refer to ‘adjectives’, though none of the examples you give actually contains any adjectives at all: they are all adjunct nouns. For hyphenation purposes, though, adjectives and adjunct nouns work the same.)
In your first example, you have such a scenario: relay networks is modified by two separate adjectives, both of which happen to be compound: dual-hop and multiple-access. (Or more precisely, as you’ve also pointed out, you have a noun phrase, multiple-access relay network, which is modified by a single compound adjective, dual-hop.) As such, no linking of the two adjectives is called for, any more than it would make sense to write “big–red relay networks” rather than just “big red relay networks” (if indeed networks had colours).
The only time you (can) use the en dash is when you have a compound adjective one or more of whose components are themselves compound phrases.
Your second example is such a case: the compounding here is between semidefinite programming (or semi-definite programming) on the left hand side, and based on the right hand side. Since semidefinite programming is an open compound in itself, and you are using it as one of the elements in a compound adjective, you have the choice of using an en dash to clarify the compounding:
Examples where both elements of the compound adjective are themselves compound adjectives are harder to come up with. The only example Chicago gives is a quasi-public–quasi-judicial body, which as they note works better if you simply take the two compound adjectives as separate: a quasi-public, quasi-judicial body (similar to your first example).