This paper proposes a novel deterministic optimization approach for the Unit Commitment (UC) problem, involving thermal generating units. A mathematical programming model is first presented, which includes all the basic constraints and a set of binary variables for the on/off status of each generator at each time period, leading to a convex mixed-integer quadratic programming (MIQP) formulation. Then, an effective solution methodology based on valid integer cutting planes is proposed, and implemented through a Branch and Cut search for finding the global optimal solution. The application of the proposed approach is illustrated with several examples of different dimensions. Comparisons with other mathematical formulations are also presented. (C) 2014 Elsevier Ltd. All rights reserved.