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

Those around George Osborne have for months been - perhaps a tad optimistically - arguing that once the economic figures turn around, then the political figures will shift too.

BBC: End to recession gives hope to coalition partners

The finalists of Euro 96 are now expected, perhaps a little over-optimistically, to go one better.

BBC: Jozef Chovanec

The combination of inflation--a debilitating disease that undermines people's sense of order and mocks sound values, such as hard work and looking optimistically toward the future--an intensely divisive war in Vietnam and the Watergate scandals had created a destructive, venomous environment when Ford took the oath of office.

FORBES: These Numbers Don't Figure