Sorafenib + Topotecan for Platinum-Resistant Recurrent Ovarian Cancer

OUTLINE: This is a multi-center study. * Topotecan: 4mg/m2 weekly, 3 weeks on and one week off. * Sorafenib: Assigned cohort dose for phase I (up to 12 patients) Maximum tolerated dose for phase II (21 total patients) Cycles will consist of 4 weeks (28 days) with disease evaluations every 8 weeks. Non-PD and acceptable toxicity: Patients will continue protocol therapy PD or unacceptable toxicity: Patients will discontinue protocol therapy ECOG performance status 0-1 Life expectancy: Three (3) months Hematopoietic: * White blood cell count (WBC) \> 3 K/mm3 * Hemoglobin (Hgb) \> 9 g/dL * Platelets \> 100 K/mm3 * Absolute neutrophil count (ANC) \> 1.5 K/mm3 * INR \< 1.5 or a PTT within normal limits. NOTE: Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. * No evidence or history of bleeding diathesis or coagulopathy. Hepatic: * Bilirubin \< 1.5 x ULN * Aspartate aminotransferase (AST, SGOT) \< 2.5 x ULN * Alanine aminotransferase (ALT, SGPT) \< 2.5 x ULN * Alkaline phosphate \< 2.5 x ULN Renal: * Creatinine \< 1.5 x ULN Cardiovascular: * No history of myocardial infarction or angina pectoris or angina equivalent within 6 months prior to registration for protocol therapy (the patient may not be on anti-anginal or anti-arrhythmic medications), or have uncontrolled hypertension or congestive heart failure \> class II NYHA Pulmonary: * No thrombolic or embolic events such as a cerebrovascular accident, including transient ischemic attacks within the past 6 months. * No pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within 28 days prior to registration for protocol therapy. * No non-pulmonary hemorrhage/bleeding event \> CTCAE Grade 3 within 28 days prior to registration for protocol therapy.