AN INTERIOR POINT CODE FOR NONLINEAR CONSTRAINED OPTIMIZATION

**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

**Authors:**

**Silvia Bonettini**

Dept. of Mathematics, University of Ferrara - ITALY,

bntslv@unife.it**Valeria Ruggiero**

Dept. of Mathematics, University of Ferrara - ITALY

rgv@unife.it

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.

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.

- 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. - Durazzi C.,
*On the Newton interior-point method for nonlinear programming problems*, J. Optim. Theory Appl.**104**(2000), 73-90. - Durazzi C., Ruggiero V.,
*Global convergence of the Newton interior--point method for nonlinear programming*, J. Optim. Theory Appl.**120**(2004), 199-208. - Bonettini S., Galligani E., Ruggiero V.,
*Inner solvers for interior point methods for large scale nonlinear programming*, to appear on Comput. Optim. Appl. (2006). - Bonettini S.,
*A nonmonotone inexact Newton method*, Optim. Meth. Software**20**(2005), 475-491 - Bonettini S., Ruggiero
V.,
*Some iterative methods for the solution of a symmetric indefinite KKT systems*, to appear on Comput. Optim. Appl. 2006. - 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). - Bonettini S.,
*Some Preconditioned Conjugate Gradient Algorithms for the Solution of Equality Constrained Quadratic Programming Problems,*submitted (2006).

Last modified: December 20, 2006.