Deterministic Global Optimization in Design , Control , and Computational

This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decomposition-based primal dual methods, (ii) methods for generalized geometric programming problems, and (iii) global optimization methods for general nonlinear programming problems. The classes of mathematical problems that are addressed range from indeenite quadratic programming to concave programs, to quadratically constrained problems, to polynomials, to general twice continuously diierentiable nonlinear optimization problems. For the majority of the presented methods nondistributed global optimization approaches are discussed with the exception of decomposition-based methods where a distributed global optimization approach is presented. 1. Background. A signiicant eeort has been expended in the last ve decades toward theoretical and algorithmic studies of applications that arise in Process Synthesis, Design, Control, and Computational Chemistry. In the last decade the area of global optimization has attracted a lot of interest from the Operations Research and Applied Mathematics community, while in the last ve years we have experienced a resurgence of interest in Chemical Engineering for new methods of global optimization as well as the application of available global optimization algorithms to important engineering problems. This recent surge of interest is attributed to three main reasons. First, a large number of process synthesis, design, control, and computational chemistry problems are indeed global optimization problems. More speciically, in the area of Process Synthesis and Design, global optimization problems arise in phase equilibrium, non-ideal separations, energy optimization, reactor-based systems, parameter estimation, data reconciliation, and metabolic reaction pathways. In the area of Process Control, global optimization issues are in the robust control analysis of systems with real parametric uncertainty, stability analysis of polytopes of matrices, optimal control of complex reaction mechamisms, and nonlinear model predictive control. In the area of Process Operations, the design of systems under uncertainty, and the planning and scheduling of batch, semi-continuous, and continuous processes result in global optimization problems. In the area of Computational Chemistry, global optimization problems arise in the clusters of atoms and molecules, the design of small organic molecules, the three-dimensional structure prediction of oligopeptides, and polypeptides, the prediction of protein structure, the interaction of proteins, the reenement of X-ray and NMR data, and the design of constrained peptides. Second, the existing local nonlinear