Unroll the carpet completely, then roll it up in the opposite direction of the kinks. Allow the carpet to sit rolled up this way for an entire day.
Place a heavy, flat object on the carpet over the kinks and bumps. Depending on the severity of the kinks, this could be a couple of heavy books or perhaps a coffee table or other large piece of furniture with a fairly flat bottom. Leave the items on the carpet for a couple of days.
Move the rug out into the sun, if possible. Temperatures between 70 and 85 degrees Fahrenheit are enough to naturally release some of the tension in the carpet. Leave the carpet out for an entire day before bringing it back inside.
Have a professional steam the carpet. Much like the sunlight, steam can release tension in the carpet. While you can use a consumer product to steam-clean the carpet yourself, a professional can diagnose the severity of the kink and take appropriate actions. Further, a professional can tell if an immovable kink is the result of a deformation in the carpet. In that case, steaming the carpet yourself would be in vain.