The purpose of this study is to investigate the anti-myeloma effect of panobinostat given at two different doses (10 mg and 20 mg oral) in combination with carfilzomib (20/56 mg/m2 i.v.) and low dose dexamethasone (20 mg oral) vs carfilzomib plus low-dose dexamethasone in patients with relapsed or relapsed and refractory multiple myeloma. Safety and efficacy will be evaluated. Treatment will be administered in 4-week cycles until patients discontinue due to disease progression or unacceptable toxicity or for other reasons.