The phrase "while striving to" is grammatically correct and can be used in written English.
It is typically used to describe an action or effort that is ongoing or continuous. Example: While striving to achieve her dream of becoming a doctor, Sarah faced many challenges along the way.
Now increase the number of push ups gradually from there, all the while striving to do some number of push ups EVERY day.
Striving to be the best is a great idea, while striving to be perfect will never work.
We've got to keep building that while striving to be the fittest and most powerful team on the circuit.
Mr. Obama often boxes careful rounds with Mrs. Clinton, rationing his jabs while striving to appear unflappable.
This is disheartening, as a school superintendent provides vision and leadership while striving to demarginalize students regardless of creed, color or ethnicity.
It said the News Corporation had tried to blame lower-ranking executives while "striving to protect more senior figures, most notably James Murdoch".
Our elected representatives, while striving to please their particular constituents, should remember that they also serve the entire nation — including those who didn't vote for them.
Haber and Hayes's aim was to give the local youth an alternative to crime that incorporated good manners and a team ethic while striving to improve individually.
Since then, he has been continually at odds with his party, while striving to please a harshly partisan right-wing press.
The book speaks to the high-achieving children of narcissistic parents, who can lose track of their own desires while striving to please.
The county's music directors have found imaginative ways to put together their programs while striving to delight, enlighten and build their audiences.
