"push higher" is a perfectly valid phrase in written English.
You could use it in a variety of contexts. For example: "We need to push higher to meet this quarter's sales targets."
Mourinho had Madrid push higher, but it didn't work.
The FTSE 100 is continuing to push higher.
He said he wondered if the market could push higher.
Wall Street is attempting to push higher, and add to Friday's recovery.
As gasoline prices push higher, S.U.V.'s are being nudged from their popularity.
BAE bucked the trend of the wider market, which failed to push higher after Friday's 10-month closing high.
Catering group Compass is the biggest faller in the FTSE 100, even as leading shares attempt to push higher.
A recovery in the mining sector is helping leading shares to push higher after three days of decline.
No matter the setting, the sixth-grade curriculum is changing, too, as teachers and parents push higher-level material like geometry and geology, a trickle-down effect from high schools, where enrollment in college-level advanced placement courses has doubled over the last decade.
Riyadh's hope was that low crude prices would push higher-cost US shale producers out of business.
With the company–and not the wholesaler controlling what the shopkeeper buys, it is possible to manage the product mix and push higher-margin products into the market.
