Wednesday's first round was pushed back by a delay of more than 3 1/2 hours with Olesen among those unable to finish the first round before play was suspended. The threat of lightning and later heavy rain Thursday stopped play with many players still on the course.
The second round is to be completed early Friday when the cut will be determined and the players regrouped by score.
Olesen is at 12-under-par 132 after 36 holes, having backed his first round 64 with a 4-under 68.
First-round co-leader Pablo Larrazabal is in a large group at 6-under but is 2-over after nine holes of the second round.
Olesen needed to finish four holes of his first round Thursday and was able to pull into a tie for the lead with Larrazabal. He had a pair of birdies in his first five holes of the second round but suffered a bogey at the 15th -- his sixth hole of the round.
After six pars, he birdied Nos. 4 and 5 and got to 4-under on the day with a birdie at the eighth hole.
Celebrity Families of 2014 [PHOTOS]