Semi-Infinite Optimization With Implicit Functions

TitleSemi-Infinite Optimization With Implicit Functions
Publication TypeJournal Article
Year of Publication2015
AuthorsStuber MD, Barton PI
JournalInd. Eng. Chem. Res.
Date Published01/2015

In this work, equality-constrained bilevel optimization problems, arising from engineering design, economics, and operations research problems, are reformulated as an equivalent semi-infinite program (SIP) with implicit functions embedded, which are defined by the original equality constraints that model the system. Using recently developed theoretical tools for bounding implicit functions, a recently developed algorithm for global optimization of implicit functions, and a recently developed algorithm for solving standard SIPs with explicit functions to global optimality, a method for solving SIPs with implicit functions embedded is presented. The method is guaranteed to converge to epsilon-optimality in finitely many iterations given the existence of a Slater point arbitrarily close to a minimizer. Besides the Slater point assumption, it is assumed only that the functions are continuous and factorable, and that the model equations are once continuously differentiable.