For a detailed description of the algorithm implemented in Interior/CG see Byrd et al., 1999  and for the global convergence theory see Byrd et al., 2000 . The method implemented in Interior/Direct is described in Waltz et al., 2006 . The Active Set algorithm is described in Byrd et al., 2004  and the global convergence theory for this algorithm is in Byrd et al., 2006a . A summary of the algorithms and techniques implemented in the Knitro software product is given in Byrd et al., 2006b .
The implementation of the CG preconditioner makes use of the icfs software, which is described in details in Lin and Moré, 1999 .
For mixed-integer nonlinear optimization, the hybrid Quesada-Grossman (HQG) method in Knitro is based on the algorithm described in . The MISQP algorithm in Knitro is Artelys’ own implementation of the MISQP algorithm described in  but differs in some details.
In order to strengthen MINLP formulations Knitro generates cuts. Especially, Knitro generates lifted cover inequalities which requires solving efficiently a knapsack problem. For solving this problem, we use the Combo algorithm from Martello et al., 1997 .
To solve linear systems arising at every iteration of the algorithm, Knitro may utilize routines MA27 or MA57 , a component package of the Harwell Subroutine Library (HSL). HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/
In addition, the Active Set algorithm in Knitro may make use of the COIN-OR Clp linear programming solver module. The version used in Knitro may be downloaded from http://www.artelys.com/tools/clp/
Lastly, Knitro may make use of the Intel(R) Math Kernel Library (https://software.intel.com/en-us/intel-mkl) for some linear algebra computations.
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R. H. Byrd, J.-Ch. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming”, Mathematical Programming, 89(1):149–185, 2000.
R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps”, Mathematical Programming A, 107(3):391–408, 2006.
R. H. Byrd, N. I. M. Gould, J. Nocedal, and R. A. Waltz, “An algorithm for nonlinear optimization using linear programming and equality constrained subproblems”, Mathematical Programming, Series B, 100(1):27–48, 2004.
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