sets one's cap at

Verb

set one's cap at (third-person singular simple present sets one's cap at, present participle setting one's cap at, simple past and past participle set one's cap at)

1. (idiomatic) To choose a man as a potential husband (for a girl).
   • To hear her rant, one would have supposed, who had not seen him, that her lank-haired, grimly partner, was the prettiest youth in the county of Dublin, and that all the comely lasses in Chapelizod and the country round were sighing and setting caps at him […]1863, Sheridan Le Fanu, The House by the Churchyard
2. (broadly, idiomatic) To choose something as a goal.
   • Patrick O'Brian, "HMS Surprise".
     How he has escaped marriage until now I cannot tell: the number of caps set in his direction would furnish a warehouse.