amodMC
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 tangentlinear mode. Subgradients are natural extensions of “usual” derivatives which allow the application of derivativebased 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 tangentlinear 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 branchandbound method. The superiority of adjoint over tangentlinear mode is illustrated by two examples. 
Homepage:  http://www.stce.rwthaachen.de/software/amodMC.html 
Programming Languages:  Fortran 
Keywords:  nonsmooth analysis; McCormick relaxations; algorithmic differentiation; adjoint mode; subgradients 
Related Software:  libMC; BARON; ANTIGONE; dcc; GRANSO; DFOTRNS; GQTPAR; DGM; HANSO; GradSamp; Eigen; MC++; MPBNGC; LINDOGlobal; PBNCGC; LINDO; Couenne; SNOPT; SCIP; modMC 
Cited in:  6 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Adjoint mode computation of subgradients for McCormick relaxations. Zbl 1253.65031 Beckers, Markus; Mosenkis, Viktor; Naumann, Uwe 
2012

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top 5
Cited by 12 Authors
Cited in 5 Serials
1  Journal of Optimization Theory and Applications 
1  Optimization 
1  Journal of Global Optimization 
1  SIAM Journal on Optimization 
1  Optimization Methods & Software 