I. To determine the maximum-tolerated doses (MTD) and dose-limiting toxicities of two different regimens of ABT-888 (veliparib) when administered with carboplatin and PLD (Doxil, Lipodox) (pegylated liposomal doxorubicin hydrochloride) in recurrent, platinum-sensitive epithelial ovarian, fallopian tube, or primary peritoneal cancer.