In this work, a collection of elliptic and parabolic control problems with control and state constraints is described, focusing on the discretization techniques which yield to Nonlinear Programming (NLP) problems having large, sparse and structured Hessian and Jacobian matrices. The collection includes 25 elliptic and parabolic control problem, which are described in detail, reporting the sparsity pattern of the Hessian and Jacobian matrices. The figures depicting the discrete solutions of the elliptic problems are also reported. The AMPL models of the elliptic control problems can be downloaded from the prof. Mittelmann's web page http://plato.asu.edu/ftp/ampl_files/ellip_ampl/ while the ones related to the parabolic ones are downloadable following the link below.

**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.

- S. Bonettini, V. Ruggiero (2006),
*A Collection of Optimal Control Problems,*pdf file (340 Kb) - Figure.zip, compressed pdf file (12,2 Mb) containing the figures of the discrete solution of the elliptic control problems.
- Parabol_ampl.zip, compressed file (3.8 Kb) containing the AMPL models of the parabolic control problems

The AMPL models of the elliptic control problems are downloadable from the prof. Mittelmann's web page http://plato.asu.edu/ftp/ampl_files/ellip_ampl/

- H. D. Mittelmann, H. D. Mittelmann (1999),
*Optimization techiques for solving elliptic control problems with control and state constraints: Part 1. Boundary control*, Computational Optimization and Applications,**16,**29-55. - H. D. Mittelmann, H. D. Mittelmann (2001),
*Optimization techiques for solving elliptic control problems with control and state constraints: Part 2. Distributed control*, Computational Optimization and Applications,**18,**141-160. - H. D. Mittelmann, H. D. Mittelmann (2000),
*Solving elliptic control problems with Interior Point and SQP Methods: control and state constraints*, Journal of Computational and Applied Mathematics,**120**, 175--195. - C. Durazzi (1998),
*Lagrangian Methods for discrete optimal control problems,*Ph.D. Thesis.

Last modified: December 19, 2006.