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 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 Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Adjoint mode computation of subgradients for McCormick relaxations. Zbl 1253.65031Beckers, Markus; Mosenkis, Viktor; Naumann, Uwe 2012 all top 5 Cited by 12 Authors 3 Khan, Kamil A. 1 Baier, Robert 1 Barton, Paul I. 1 Beckers, Markus 1 Farkhi, Elza M. 1 Larson, Jeffrey 1 Menickelly, Matt 1 Mosenkis, Viktor 1 Naumann, Uwe 1 Roshchina, Vera 1 Watson, Harry A. J. 1 Zhou, Baoyu 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 Cited in 5 Fields 5 Operations research, mathematical programming (90-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Real functions (26-XX) 3 Numerical analysis (65-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year