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journal contribution
posted on 2011-08-01, 00:00 authored by John N. HookerWe investigate some approaches to solving nonconvex global
optimization problems by convex nonlinear programming methods. We
assume that the problem becomes convex when selected variables are
fixed. The selected variables must be discrete, or else discretized if they
are continuous. We provide a survey of disjunctive programming with
convex relaxations, logic-based outer approximation, and logic-based Benders
decomposition. We then introduce a branch-and-bound method with
convex quasi-relaxations (BBCQ) that can be effective when the discrete
variables take a large number of real values. The BBCQ method generalizes
work of Bollapragada, Ghattas and Hooker on structural design
problems. It applies when the constraint functions are concave in the
discrete variables and have a weak homogeneity property in the continuous
variables.