The optimization of process systems with complex investment cost functions, defined over several intervals of equipment sizes, operating pressures and temperatures, is addressed in this paper. The discontinuities with respect to these variables are modeled with disjunctions that are converted into tight mixed-integer constraints with the convex hull formulation for each disjunction. The efficiency of the resulting MINLP model for fixed structures is shown on a flowsheet optimization problem and compared with the big-M formulation. To address the structural optimization of process flowsheets, we propose a generalized disjunctive programming algorithm (GDP) in which the complex investment cost functions are formulated as embedded disjunctions. The GDP algorithm consists of MINLP subproblems for the optimization of fixed flowsheet structures and MILP master problems to predict new flowsheets to be optimized. The proposed algorithm is tested on the synthesis of a process network with nine units, and the synthesis of a vinyl chloride monomer production process consisting of 32 process units. It is shown that the proposed GDP algorithm is rigorous for handling discontinuities in complex cost functions, and is robust and efficient for structural flowsheet optimization problems.