(253h) Subtangent-Based Approaches for Optimization of Parametric Process Systems

Several established methods for deterministic global optimization typically compute useful global bounding information by constructing and minimizing convex underestimators of parametric process models. Convex underestimators (and analogous concave overestimators) are also useful in their own right for reachable-set methods, design centering, and constructing useful simpler approximations of complicated process models.

This presentation examines linear “subtangents” of nonlinear convex underestimators of process models, constructed from the original underestimators using subgradient evaluations. Subtangents are weaker relaxations than the original underestimators, yet are straightforward to analyze and generally inexpensive to compute. It is shown that, under mild assumptions, subtangents inherit second-order convergence properties from the original underestimators, and are therefore guaranteed to be useful in applications in their own right [3]. This result is strengthened further if the original underestimators are sufficiently smooth, as is true of the differentiable McCormick relaxations [2] and the αBB relaxations [1]. These results are applied to yield powerful bounding methods involving bundles of subtangents, which are particularly effective in cases where evaluating the original convex underestimators is computationally expensive. Implications and examples are discussed.

References

[1] CS Adjiman, S Dallwig, CA Floudas, and A Neumaier, A global optimization method, αBB, for general twice-differentiable constrained NLPs: I. Theoretical advances, Comput. Chem. Engng, 22:1137-1158, 1998.

[2] KA Khan, HAJ Watson, and PI Barton, Differentiable McCormick relaxations, J. Glob. Optim., 67:687-729, 2017.

[3] KA Khan, Subtangent-based approaches for dynamic set propagation, submitted, 2018.