S. Bonettini     V. Ruggiero


IP-PCG is a C++ software designed to solve large-scale Nonlinear Programming Problems (NLP). It employs a Newton inexact interior point algorithm [1, 2, 3, 4] with a line search strategy based on the Eisenstat and Walker rule, even in the nonmonotone case [5]. At each step of the interior point algorithm, a perturbation of the Newton equation is solved by the Preconditioned Conjugate Gradient (PCG) method, with a suitable indefinite preconditioner [6, 7, 8]. The preconditioner is factorized in a Cholesky like form by means of the BLKFCLT routine. The currently implemented IP-PCG is provided of a partial AMPL interface


This work is supported by the Italian FIRB Project
Parallel Algorithms and Numerical Nonlinear Optimization (grant RBAU01JYPN), http://dm.unife.it/pn2o
and by the Italian M.I.U.R. Project
Numerical Methods and Mathematical Software in Applications (grant 2004012559), http://www.math.unifi.it/~brugnano/Cofin2004.

Instructions and documentation

The compressed file ip_pcg (590 KB) contains the binary version  for the Itanium 2 platform running HP-UX operating system, compiled with the +Ofaster option by the aCC compiler. 

The executable file should be called from the command line as follows

./ip_pcg stub.nl [options]

where stub.nl is the AMPL generated .nl file of an NLP problem. A detailed description of the output and of the user available options can be found here.

Remark: if you use our code then you are kindly asked to cite this page, together with the references [4] and [7] here below.

Additional information

  1. El--Bakry A.S., Tapia R.A., Tsuchiya T., Zhang Y., On the formulation and theory of Newton interior--point method for nonlinear programming, J. Optim. Theory Appl. 89 (1996), 507-541.
  2. Durazzi C., On the Newton interior-point method for nonlinear programming problems, J. Optim. Theory Appl. 104 (2000), 73-90.
  3. Durazzi C., Ruggiero V., Global convergence of the Newton interior--point method for nonlinear programming, J. Optim. Theory Appl. 120 (2004), 199-208.
  4. Bonettini S., Galligani E., Ruggiero V.,  Inner solvers for interior point methods for large scale nonlinear programming, to appear on Comput. Optim. Appl. (2006).
  5. Bonettini S., A nonmonotone inexact Newton method, Optim. Meth. Software 20 (2005), 475-491
  6. Bonettini S., Ruggiero V., Some iterative methods for the solution of a symmetric indefinite KKT systems, to appear on Comput. Optim. Appl. 2006.
  7. Bonettini S., Ruggiero V., Tinti F., On the Solution of Indefinite Systems Arising in Nonlinear Optimization, Technical Report n.359, Dept. of Mathematics, University of Ferrara (2006).
  8. Bonettini S., Some Preconditioned Conjugate Gradient Algorithms for the Solution of Equality Constrained Quadratic Programming Problems, submitted (2006).

Last modified: December 20, 2006.