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.
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.
R. H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large scale nonlinear programming”, SIAM Journal on Optimization, 9(4):877–900, 1999.
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.
R. H. Byrd, N. I. M. Gould, J. Nocedal, and R. A. Waltz, “On the convergence of successive linear-quadratic programming algorithms”, SIAM Journal on Optimization, 16(2):471–489, 2006.
R. H. Byrd, J. Nocedal, and R.A. Waltz, “KNITRO: An integrated package for nonlinear optimization”, In G. di Pillo and M. Roma, editors, Large-Scale Nonlinear Optimization, pages 35–59. Springer, 2006.
I. Quesada, and I. E. Grossmann, “An LP/NLP based branch and bound algorithm for convex MINLP optimization problems”, Computers and Chemical Engineering, 16(10-11):937–947, 1992.
O. Exler, and K. Schittkowski, “A trust-region SQP algorithm for mixed-integer nonlinear programming”, Optimization Letters, Vol. 1:269–280, 2007.
R. H. Byrd, J. Nocedal, and R. A. Waltz, “Feasible interior methods using slacks for nonlinear optimization”, Computational Optimization and Applications, 26(1):35–61, 2003.
R. Fourer, D. M. Gay, and B. W. Kernighan, “AMPL: A Modeling Language for Mathematical Programming”, 2nd Ed., Brooks/Cole – Thomson Learning, 2003.
Hock, W. and Schittkowski, K. “Test Examples for Nonlinear Programming Codes”, volume 187 of Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, 1981.
J. Nocedal and S. J. Wright, “Numerical Optimization”, Springer Series in Operations Research, Springer, 1999.
C.-J. Lin and J. J. Moré, “Incomplete Cholesky factorizations with limited memory”, SIAM J. Sci. Comput., 21(1):24–45, 1999.
Harwell Subroutine Library, “A catalogue of subroutines (HSL 2002)”, AEA Technology, Harwell, Oxfordshire, England, 2002.