I was trying now for a few hours, no chance. As seen on the screenshot, I want to deform that triangle 3-dimensionally so that it looks a bit like a tent. The red marked edge and vertex on the opposing side (the anchors) have to stay right in place because I apply other modifiers in the next steps. I too apply the Mirror Modifier which is active on that screenshot.
I want to deform it as follows: the orange edge has to be deformed on the "Z" and "Y" coordinates to get the shape a little bit like the yellow curve. Same with the turquoise edge to its corresponding curve on the "X" and "Y" axis. The rest of the vertices have to follow proportionally. Well... I tried it manually by proportional editing, but that would be very difficult to achieve what I want.
EDIT: I edited my question so it would be understandable without a picture.