### Browsing by Author "Grossmann, I.E."

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Item Decomposition Strategy for Designing Flexible Chemical Plants.(1987) Grossmann, I.E.; Halemane, K.P.; ISROne of the main computational problems faced in the optimal design of flexible chemical plants with multi-period operation is the large number of decision variables that are involved in the corresponding nonlinear programming formulation. To overcome this difficulty, a decomposition technique based on a projection- restriction strategy is suggested to exploit the block-diagonal structure in the constraints. Successful application of this strategy requires an efficient method to find an initial feasible point, and the extension of current equation ordering algorithms for adding systematically inequality constraints that become active. General trends in the performance of the proposed decomposition technique are presented through an example.Item Optimal Process Design Under Uncertainty.(1987) Halemane, K.P.; Grossmann, I.E.; ISRA rigorous mathematical formulation is presented for the problem of optimal design under uncertainty. This formulation involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region. To circumvent the problem of infinite dimensionality in the constraints, an equivalence for the feasibility condition is established which leads to a max-min-max constraint. It is shown that if the inequalities are convex, only the vertices in the polyhedron need to be considered to satisfy this constraint. Based on this feature, an algorithm is proposed which uses only a small subset of the vertices in an iterative multiperiod design formulation. Examples are presented to illustrate the application to flexible design problems.Item Optimization Strategies for Flexible Chemical Processes.(1987) Grossmann, I.E.; Halemane, K.P.; Swaney, R.E.; ISRThe objective of this paper is to give an overview of the optimization strategies that are required when designing chemical processes in which the existence of regions of feasible steady- state operation must be ensured in the face of parameter variations. Two major areas are considered: optimal design with a fixed degree of flexibility, and design with optimal degree of flexibility. For the first area the problems of multiperiod design, and design under uncertainty are analyzed. For the second area the problem of deriving an index of flexibility in the context of multiobjective optimization is discussed. As shown in the paper, the major challenge in these problems lies in the development of efficient solution procedures for large scale nonlinear programs which are either highly structured, or otherwise involve an infinite number of constraints.