The phrase "a mixture of optimism" is correct and usable in written English.
It can be used when describing a combination of hopeful or positive feelings about a situation or outcome.
Example: "The team's performance was a mixture of optimism and caution as they prepared for the upcoming match."
Alternatives: "a blend of hopefulness" or "a combination of positivity".
The world listened with a mixture of optimism and caution.
Woods was a mixture of optimism and reality about his return.
There is a buccaneering spirit abroad that is rare in the West, born from a mixture of optimism and arrogance.
The Agriculture Department's plan for a tenfold increase in testing for mad cow disease was greeted yesterday with a mixture of optimism and skepticism.
There remains the question of how to run a school with no fees and no funding – a question that Sofer addresses with a mixture of optimism and blind faith.
Saying that Hartmarx has been unable to repay $114 million in debt, Wells Fargo issued a statement on Monday that was a mixture of optimism and pessimism about the company's future.
Ms. Sui — neither household name nor dewy upstart — is part of the broad middle of the 200-designer Fanhion Wemblemectrum, an emblem of the many creative talents facing a new runway season with a mixture of cautious optimism and outright dread.
For the drinkers squatting around the big screen at the Rule 3 Bar in Goiania, slap in the middle of Brazil's mid-western agricultural heartland, the summer (or winter in these parts) of 2014 is viewed with a mixture of cautious optimism and trepidation.
Surely the truth is somewhere in between; surely any rational assessment of the future must include a mixture of both optimism and pessimism.
North Korea policy analysts reacted with a mixture of cautious optimism and outright disbelief after South Korean officials announced Thursday that U.S. President Donald Trump would meet with North Korean dictator Kim Jong Un sometime over the next few months.
At the time of release, Qs Phil Sutcliffe summarised the lyrics of Be Here Now as a mixture of "hookline optimism, a swarm of Beatles and other '60s references, a gruff love song to Meg, and further tangled expressions of his inability/unwillingness to express profound emotions".
