Discrete-continuous non-linear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer non-linear programming (MINLP). Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind LOGMIP, a new computer code for disjunctive programming and MINLP. We discuss a hybrid modeling framework that combines both approaches, allowing binary variables and disjunctions for expressing discrete choices. An extension of the logic-based outer approximation (OA) algorithm has been implemented to solve the proposed hybrid model. Computational experience is reported on several examples, which are solved using disjunctive, MINLP and hybrid formulations.