Queen's gambit accepted: holding the pawn.

I'm not understanding.  Could you please make a diagram or something so I can have a visual aid?

I think it was Bronstein who introduced me (in a commentary) to that idea. He played it against a computer who played a very rare variation which kept the pawn. Bronstein though: ¨This is called the Queen's Gambit. Lets gambit that pawn then!¨ (Or something like that). He won a fine attacking game (back in the days where computers were weaker than strong GMs).

Ever see this one?

No, but I have seen similar.

It is not a gambit.

The real problem with 3. e4, and even with 3. e3 is that black can play 3. e5! and black has a good game.

That is why the main move is 3. Nf3, avoiding the e5 move.

Well, it's still unclear if black can equalize in the e5 line.

The "answer" is in post #15, and the dozens of other threads on exactly this same question.

Can't you guys read (and comprehend) what's already in front of you??

3) e4  e5, is a sharp (and popular) mainline, FOR BOTH SIDES!

Yes, 3e4 is perfectly good, and responses played by strong players as well as 3...e5 include 3...Nf6, 3...Nc6 and even 3....c5. The moves 3...b5, and 3...Be6 mentioned by the OP are typical "Newbie fail" attempts which concentrate on hanging onto the pawn, rather than developing rapidly, and fighting for share of centre.

Irontiger your mainline in post #15 is wrong.

and some example with 4...b4

Your final evaluation of the 5.Nc3 b4 variation of "drawish at best" is wrong. White will retake on c4 without much trouble, and Black has weak squares on c4 and c5. (not a huge advantage though, but still some advantage)

As for 4.a4 b4, 6...c5 followed by ...Nc6 is already a serious improvement over your line.

After 5.Nc3 b4 the game is equal. After my 5.e3 white has an advantage.

I'm not one who blindly follows engine evaluation but there's more than 1 full point of difference between the two moves. And I would say mine is even easier to play, how do you like your stranded knight?

In the second 6...c5 would be followed by black resigning, not by ...Nc6.

6...c5? Bxc4 Nc6?? Ng5 and the game is over, for example e6 Qf3 with a fork, or Nh6 Qf3 with another fork.

What about 

The good way to hold c4 is to prepare b5 with a6 :

Black will be better placed after something like 4.e3 b5 where it is not easy for white to recover the pawn.

As usual white has to play b3 and black will give the pawn back.

This is a Svidler's speciality, and many GM play this line to make an easy draw.

The reference game begin Svidler-Aronian :

White can deviate and try to improve at some point, but for the moment, we don't know how to find an advantage for white in this line.

This was/is the reason of the resurrection of 3.e3 and 3.e4 but again, black has concrete ways to defend/fight.

I think we see more and more 1.d4 and 2.Nf3 or 1.Nf3 and 2.d4 more often because it avoids this move order for black.

That's why you play e3 instead of e4, so after c6 you play axb5, and if cxb5, then Qf3.

This is the only post you need to know on how to deal with that position.

Observe this simple trap: