Improved Convex Underestimators and Hybrid Methods for Deterministic Global Optimization

Princeton University, Princeton NJ

Investigators

Abstract

Intellectual Content: The primary objective of this research is to develop novel theoretical, algorithmic and computational techniques for global optimization problems that arise in a variety of chemical engineering process design, synthesis and operations problems. It is the PI's intention to investigate (i) the development of a new class of improved convex underestimators for twice-continuously differentiable constrained nonlinear programming problems which will enhance the aBB approach and will be applied in a variety of phase equilibrium, design and synthesis problems; (ii) the theoretical and algorithmic development of a novel cut and splice refinement of the aBB convex subfunctional that will result in new types of tigher convex underestimators; (iii) the theoretical and algorithmic issues for the development of novel trigonometric convex underestimators for several classes of nonconvex trigonometric functions; and (iv) the development of new hydrid global optimization methods which combine the beneficial elements of the enhanced aBB deterministic global optimization framework with stochastic based approaches, and their distributed computing implementations, and their applications to medium and large-scale nonconvex optimization problems that arise in pooling and blending applications. Broader Impact: The integration of research and education will be enhanced through the introduction of lecture material and projects in the elective graduate course on Nonlinear Mixed Integer Optimization, and the required capstone senior design course Design, Synthesis and Optimization of Chemical Processes. The research will broaden the participation of underrepresented groups since it will aim at attracting female and minority students at the graduate level and the undergraduate senior theses level. The results of the work will be broadly disseminated to researchers in academia and industry through presentations at domestic and international meetings, scholarly refereed journal publications and through our web page (http://titan.princeton.edu) which will describe the approaches, implementations and results. Many petrochemical, chemical, pharmaceutical and services/software companies will benefit by the development of rigorous global optimization methods that can address important problems in process design and operations. This can lead to faster response to the market demands, and hence more efficient use of the processing facilities, which has direct benefit on the US economy.