swMATH ID: 6614
Software Authors: Beckers, Markus; Mosenkis, Viktor; Naumann, Uwe
Description: Adjoint mode computation of subgradients for McCormick relaxations In [{it A. Mitsos}, {it B. Chachuat} and {it P. I. Barton}, SIAM J. Optim. 20, No. 2, 573–601 (2009; Zbl 1192.65083)], a method similar to Algorithmic Differentiation (AD) is presented which allows the propagation of, in general nondifferentiable, McCormick relaxations [see, e.g., {it G. P. McCormick}, Math. Program. 10, 147–175 (1976; Zbl 0349.90100)] of factorable functions and of the corresponding subgradients in tangent-linear mode. Subgradients are natural extensions of “usual” derivatives which allow the application of derivative-based methods to possibly nondifferentiable convex and concave functions. The software package libMC [Mitsos et. al., loc. cit.] performs the automatic propagation of the relaxation and of corresponding subgradients based on the principles of tangent-linear mode AD by overloading. Similar ideas have been ported to Fortran yielding modMC as part of our ongoing collaboration with the authors of Mitsos et al. [loc. cit.]. par In this article an adjoint method for the computation of subgradients for McCormick relaxations is presented. A corresponding implementation by overloading in Fortran is provided in the form of amodMC. The calculated subgradients are used in a deterministic global optimization algorithm based on a branch-and-bound method. The superiority of adjoint over tangent-linear mode is illustrated by two examples.
Homepage: http://www.stce.rwth-aachen.de/software/amodMC.html
Programming Languages: Fortran
Keywords: non-smooth analysis; McCormick relaxations; algorithmic differentiation; adjoint mode; subgradients
Related Software: libMC; BARON; ANTIGONE; dcc; GRANSO; DFO-TRNS; GQTPAR; DGM; HANSO; GradSamp; Eigen; MC++; MPBNGC; LINDOGlobal; PBNCGC; LINDO; Couenne; SNOPT; SCIP; modMC
Cited in: 6 Publications

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