In this paper we present nonlinear optimization models for the optimal synthesis of heat integrated distillation sequences. These nonlinear optimization models can overcome problems with singularities that are encountered in the mixed integer nonlinear programming (MINLP) superstructure optimization of distillation columns with nonlinear short-cut models. The proposed optimization models are obtained from a systematic modeling procedure where generalized disjunctive programming models are derived using the state task network (STN) or state equipment network (SEN) superstructure representations. These models are solved with a modified logic-based outer approximation (OA) algorithm, in which the key item is an effective scheme for initialization for setting up the master problem. For heat integration, a disjunctive mixed integer linear programming (MILP) model based on pinch candidate selection is used that can be readily incorporated into the synthesis models. Numerical results are presented for both the state task network and the state equipment network representations, and for the case of no heat integration and with heat integration. As will be shown, robustness and efficiency of the structural optimization is greatly enhanced.