When: May 5, 2017, 2:00 PM
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Global Optimization of Nonconvex Nonlinear
In this paper we address the global optimization of nonconvex nonlinear generalized disjunctive programming (GDP) problems that include for instance bilinear, concave and linear fractional terms. In order to solve these nonconvex problems a convex nonlinear GDP relaxation is obtained by using suitable convex envelopes for the nonconvex terms. In order to predict tighter lower bounds to the global optimum we consider a sequence of basic steps for the convex relaxation that take a disjunctive set to another one with fewer conjuncts. We show that the strength of these bounds increases as the number of conjuncts decreases leading to a hierarchy of relaxations. Based on this procedure for strengthening lower bounds, we describe two major solution methods for globally optimizing nonconvex GPD problems. One relies on a disjunctive branch and bound algorithm that makes use of bound contraction, logic inference and a spatial branch and bound search. The other solution method relies on a logic-based outer-approximation algorithm that involves the solution of mixed-integer linear programming master problems and nonlinear programming subproblems for which new cuts are proposed, as well as a two-stage partition. A number of basic theoretical properties are proved for the proposed methods, and we illustrate the application of these methods in the global optimization of several process systems to demonstrate the computational savings that can be achieved with the tighter lower bounds.
Prof. Ignacio E. Grossmann is the Rudolph R. and Florence Dean University Professor of Chemical Engineering, and former Department Head at Carnegie Mellon University. He obtained his B.S. degree in Chemical Engineering at the Universidad Iberoamericana, Mexico City, in 1974, and his M.S. and Ph.D. in Chemical Engineering at Imperial College in 1975 and 1977, respectively. After working as an R&D engineer at the Instituto Mexicano del Petróleo in 1978, he joined Carnegie Mellon in 1979. He was Director of the Synthesis Laboratory from the Engineering Design Research Center in 1988-93. He is director of the “Center for Advanced Process Decision-making” which comprises a total of 20 petroleum, chemical and engineering companies. Ignacio Grossmann is a member of the National Academy of Engineering , Mexican Academy of Engineering, and associate editor of AIChE Journal and member of editorial board of Computers and Chemical Engineering, Journal of Global Optimization, Optimization and Engineering, Latin American Applied Research, and Process Systems Engineering Series. He was Chair of the Computers and Systems Technology Division of AIChE, and co-chair of the 1989 Foundations of Computer-Aided Process Design Conference and 2003 Foundations of Computer-Aided Process Operations Conference. He is a member of the American Institute of Chemical Engineers, Institute for Operations Research and Management Science, Mathematical Optimization Society, and American Chemical Society.