Raise a single number
JavaScript (ES6), 41 40 39 38 bytes

Saved a byte thanks to @Neil, another thanks to @user81655

x=&gt;x.map(c=&gt;c&lt;x[++i]&gt;d?x[d=i]:c,d=i=0)


Just when it seems reduceRight might finally have a chance, .map shows up yet again...