An adverbial objective a noun that functions as an adverb.
Often, the noun, as an adverb, modifies a verb, for example, "He went home". I understand "Home", here, as being the adverbial objective, for it expresses a relation of place.
In the titular sentence, however, I don't understand what the adverbial objective is. Is it supposed to be "considering" or "worth considering"?
Worth is somewhat a controversial word, there is a dispute about it being an adjective or a preposition (especially in sentences like It is worth two dollars). McCawley, R. Hyddleston and G. Pullum call it an adjective.
I don't see any NOUN in your sentence that functions as an adverb modifying a verb. In
The proposal is worth considering.
H&P say that worth is an adjective functioning as a predicate, while considering is a hollow gerund-participial that functions as a complement of the adjective worth. (See The Cambridge Grammar of the English Language, pp. 546 and 607)
There is no "adverbial objective"
In “He went home” “Home” is an uncountable noun acting as the adverbial complement of “went” (sometimes called a dative, as in “He went to home.")
In “The proposal is worth considering”, “worth considering” is an adjectival phrase and a complement.
Considering is a gerund, (“The proposal is worth your/his/our, etc. considering”) and could be substituted for “consideration”.
Worth takes on a prepositional function: compare
“The proposal is {under consideration}”.
“The proposal is {worth considering}”
Under the entry for “worth adj.” in the OED is the comment:
“Chiefly (and now only) in predicative use, or following a noun as part of a qualifying phrase. In modern English worth is non-gradable and sometimes regarded as a preposition. I. Having a specified value.
