REGIMEN III: Patients receive paclitaxel IV over 3 hours on day 1 and intraperitoneally (IP) on day 8, and cisplatin IP on day 1 or 2. Patients also receive bevacizumab and veliparib as in Regimen I. Treatment repeats every 21 days for 6 courses. Patients then receive bevacizumab alone on day 1. Treatment repeats every 21 days for 16 courses in the absence of disease progression or unacceptable toxicity.