Both sides have spoken optimistically about the talks.

双方都对本次会谈表示乐观。

《柯林斯英汉双解大词典》

I then made some groundless remarks, assessing the situation over-optimistically.

我当时放了空炮，对形势作出了过于乐观的分析。

《新英汉大辞典》

Go your way optimistically.

乐观地走自己的路。

youdao

Considering the current system's rate of return, the DJI equivalent would be, very optimistically, around 20, 000.

FORBES: Fact and Comment

More optimistically, the Net Geners are much more positive than their predecessors about their family.

ECONOMIST: The net generation

TechCrunch optimistically assumes this means Facebook is going to start slapping nosy employers with lawsuits.

FORBES: Facebook Doesn't Want Employers Asking For Users' Passwords