0. Commented References

[1]    Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. "An interior point algorithm for large-scale nonlinear programming." SIAM Journal on Optimization 9.4 (1999): 877-900.

      Main paper describing the method.

[2]   Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006).

      Excellent book on optimization that contains most of the theory needed to understand what is being implemented.

[3]    Byrd, Richard H., Jean Charles Gilbert, and Jorge Nocedal. "A trust region method based on interior point techniques for nonlinear programming." Mathematical Programming 89.1 (2000): 149-185.

      Preliminary paper describing the method and its framework. Contains a global analysis of the algorithm.

[4]     Byrd, Richard H., Guanghui Liu, and Jorge Nocedal. "On the local behavior of an interior point method for nonlinear programming." Numerical analysis 1997 (1997): 37-56.

      Describe the local behaviour of the algorithm and gives sufficient conditions to obtain superlinear convergence.

[5]    Gould, Nicholas IM, Mary E. Hribar, and Jorge Nocedal. "On the solution of equality constrained quadratic programming problems arising in optimization." SIAM Journal on Scientific Computing 23.4 (2001): 1376-1395.

      Paper describing techniques to cope with roundoff errors that results from solving equality-constrained programming (EQP) problems using the projected CG method. The projected CG method is an important substep of the method being implemented and this corrections are important to the behaviour of the interior-point method as a hole. I have written a blog post about this (link).

[6]    Byrd, Richard, Jorge Nocedal, and Richard Waltz. "Knitro: An Integrated Package for Nonlinear Optimization." Large-scale nonlinear optimization (2006): 35-59.

      Paper describing the Knitro package that, among other methods, implements the method we intend to implement in Python, internally referred as KNITRO/CG solver.

[7]    Nocedal, Jorge, Figen Öztoprak, and Richard A. Waltz. "An interior point method for nonlinear programming with infeasibility detection capabilities." Optimization Methods and Software 29.4 (2014): 837-854.

      Paper describing improvements in order to cope with infeasibility.

[8]    Waltz, R. A., J. L. Morales, J. Nocedal, and D. Orban. "An interior algorithm for nonlinear optimization that combines line search and trust region steps." Mathematical Programming, Vol 107, No. 3, 2006, pp. 391–408.

      This paper describe another interior point implementation from Nocedal. This implementation is the one used in KNITRO/DIRECT and also in Matlab interior point method (link). This implementation employs line search method, except when the KKT matrix is singular, and in this case it switches to a trust-region step (similar to the one described on previous papers).

[9]    Plantenga, Todd. "A trust region method for nonlinear programming based on primal interior-point techniques." SIAM journal on Scientific Computing 20.1 (1998): 282-305.

      This paper describe a trust-region interior point that have lots of similarities with [1]. I believe this paper had a huge influence in [1].

[10]    Istvan Maros and Csaba Meszaros "A repository of convex quadratic programming problems", Optimization Methods and Software (OMS) Volumes 11&12 (December, 1999), 671-681

      Some convex QP problems I used for test.

[11]    Dolan, Elizabeth D., Jorge J. Moré, and Todd S. Munson. "Benchmarking optimization software with COPS 3.0." Argonne National Laboratory Research Report (2004).

      Set of nonlinearly constrained optimization problems.

[12]    Marucha Lalee, Jorge Nocedal, and Todd Plantenga. "On the implementation of an algorithm for large-scale equality constrained optimization." SIAM Journal on Optimization 8.3 (1998): 682-706.

      Preliminary paper describing Byrd-Omojokun SQP method.

[13]    Gould, Nicholas IM, Dominique Orban, and Philippe L. Toint. "CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization." Computational Optimization and Applications 60.3 (2015): 545-557.

      Large optimization problem collection.