Global optimization of bounded factorable functions with discontinuities
Name
10898_2013_60_ReferencePDF.pdf
Size
670.99 KB
Format
Adobe PDF
Checksum (MD5)
7e22096be29669b5b02dc77d3b9ee195
Author(s)
Wechsung, Achim
Barton, Paul I.
Date Issued
March 2013
Journal
Journal of Global Optimization
Publisher
Springer US
Citation
Wechsung, Achim, and Paul I. Barton. “Global Optimization of Bounded Factorable Functions with Discontinuities.” Journal of Global Optimization 58.1 (2014): 1–30.
Version
Author's final manuscript
Abstract
A deterministic global optimization method is developed for a class of discontinuous functions. McCormick’s method to obtain relaxations of nonconvex functions is extended to discontinuous factorable functions by representing a discontinuity with a step function. The properties of the relaxations are analyzed in detail; in particular, convergence of the relaxations to the function is established given some assumptions on the bounds derived from interval arithmetic. The obtained convex relaxations are used in a branch-and-bound scheme to formulate lower bounding problems. Furthermore, convergence of the branch-and-bound algorithm for discontinuous functions is analyzed and assumptions are derived to guarantee convergence. A key advantage of the proposed method over reformulating the discontinuous problem as a MINLP or MPEC is avoiding the increase in problem size that slows global optimization. Several numerical examples for the global optimization of functions with discontinuities are presented, including ones taken from process design and equipment sizing as well as discrete-time hybrid systems.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10898-013-0060-3
