Differentiable McCormick relaxations
Name
10898_2016_440_ReferencePDF.pdf
Size
440.98 KB
Format
Adobe PDF
Checksum (MD5)
9f636c1312ea24a9fc470d80c5bc8e3b
Author(s)
Khan, Kamil A.
Watson, Harry Alexander James
Barton, Paul I
Date Issued
May 2016
Journal
Journal of Global Optimization
Publisher
Springer US
Citation
Khan, Kamil A., Harry A. J. Watson, and Paul I. Barton. “Differentiable McCormick Relaxations.” Journal of Global Optimization 67, no. 4 (May 27, 2016): 687–729.
Version
Author's final manuscript
Abstract
McCormick’s classical relaxation technique constructs closed-form convex and concave relaxations of compositions of simple intrinsic functions. These relaxations have several properties which make them useful for lower bounding problems in global optimization: they can be evaluated automatically, accurately, and computationally inexpensively, and they converge rapidly to the relaxed function as the underlying domain is reduced in size. They may also be adapted to yield relaxations of certain implicit functions and differential equation solutions. However, McCormick’s relaxations may be nonsmooth, and this nonsmoothness can create theoretical and computational obstacles when relaxations are to be deployed. This article presents a continuously differentiable variant of McCormick’s original relaxations in the multivariate McCormick framework of Tsoukalas and Mitsos. Gradients of the new differentiable relaxations may be computed efficiently using the standard forward or reverse modes of automatic differentiation. Extensions to differentiable relaxations of implicit functions and solutions of parametric ordinary differential equations are discussed. A C++ implementation based on the library MC++ is described and applied to a case study in nonsmooth nonconvex optimization.
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/s10898-016-0440-6
