Italian FIRB Project on 
 Parallel Algorithms and Numerical Nonlinear Optimization 



This section collects all the software produced o coauthored by members of the project research units.
The software available through the section is largely described in papers published with the project support: please, visite the related Papers section.

Available software

  • GKLS generator

    Authors: M. Gaviano, D.E. Kvasov, D. Lera, Ya.D. Sergeyev

    Topic: Software for generation of classes of test functions with known local and global minima for global optimization (published in M. Gaviano, D.E. Kvasov, D. Lera, Ya.D. Sergeyev, Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization, ACM Transactions on Mathematical Software, 29(4), 2003, pp. 469-480)

    Description: Development of numerical algorithms for global optimization is strongly connected to the problem of construction of test functions for studying and verifying validity of these algorithms. Many of global optimization tests are taken from real-life applications and for this reason a  complete information about them is not available. It often happens that there are not known a priori the number of local minima present in the problem, their locations, regions of attraction, and even values  (including that one of the global minimum).
    The GKLS generator is a procedure for generating three types (non-differentiable, continuously differentiable and twice continuously  differentiable) of classes of test functions with known local and global minima for multiextremal multidimensional box-constrained global optimization.

  • TESTVIPs - A Matlab collection of Variational Inequality Problems

    Authors: F. Tinti

    Topic: The MatLab files implementing several variational inequality problems and nonlinear complementarity problems arising from the literature are given.

    Description: We consider the following test problems:

    • Mathiesen's problem
    • Kojima Shindo's problem
    • Harker's Nash-Cournot problem
    • Pang & Murphy's Nash-Cournot problem
    • Braess Network problem
    • User OPT problem
    • HpHard problem.
    Each VIP or NCP is implemented in two files: the first contains the parameters and the definition of the feasible region of the problem and the second is the M-function file to compute the value of the map related to the problem.

  • MECVIPs - Matlab codes of extragradient methods for VIPs

    Authors: F. Tinti

    Topic: MatLab codes implementing extragradient-type methods for pseudomonotone variational inequality problems.

    Description: We give several MatLab scripts implementing some extragradient-type methods. In particular the considered methods are:

    • Extragradient method with constant steplength;
    • Extragradient method with adaptive steplegth (Marcotte's version);
    • Extragradient method with adaptive steplegth (first modified version);
    • Extragradient method with adaptive steplegth (second modified version);
    • Projection-Contraction method (Solodov-Tseng);
    • Hyperplane projection method (Solodov-Svaiter).
    These codes can be evaluated using the MatLab test problems collected in TESTVIPs. The Matlab implementation of the above methods enables us to easily change the parameters, pointing out the effectiveness and the features of each algorithm.

  • GPDT - Gradient Projection-based Decomposition Technique  [Last updated: October 2006]

    Authors: T. Serafini, L. Zanni, G. Zanghirati

    Topic: Software for convex quadratic programs arising in training the learning methodology Support Vector Machines
    - Hessian matrix: dense and large (bigger than 104)
    - Constraints: box and a single linear equality constraint

    Description: decomposition technique based on a sequence of QP subproblems of smaller size (about 103).
    Two Gradient projection methods for the smaller QP subproblems are available:
    - GVPM (Generalized Variable Projection Method)
       linesearch strategy: limited minimization rule
       steplength selection: adaptive switch between the two Barzilai-Borwein rules
    - DFGPM (Dai-Fletcher Nonmonotone Gradient Projection Method)
       linesearch strategy: nonmonotone linesearch
       steplength selection: modified Barzilai-Borwein rule
       - serial: standard C++
       - parallel: standard C++ and MPI communication routines
    Tested platform
       - serial: Intel-based PC, Digital-Alpha and HP-Itanium2 workstations
       - parallel: Cray T3E, IBM Xeon-based Linux cluster system, IBM Power5-based AIX cluster.
    Benchmark test problems:
       - MNIST database of handwritten digits
       - UCI Adult database income prediction
       - Text categorization

  • BLKFCLT - Regularized Cholesky-like factorization for sparse symmetric matrices  [Last updated: October 2005]

    Authors: S. Bonettini, V. Ruggiero

    Topic: Collection of Fortran 90 subroutines for the factorization and the solution of systems that admit a Cholesky-like factorization. The code is based on a modification of the package by Ng and Peyton (included in the LIPSOL 0.3 package), that performs the Cholesky factorization of a positive definite matrix.

  • IP-PCG - An interior point algorithm with the PCG method as inner solver [Last updated: December 2006]

    Authors: S. Bonettini, V. Ruggiero

    Topic: Software for nonlinear constrained optimization.
    - Hessian matrix: sparse and large
    - Constraints: box, equality and inequality.

    Description: Inexact Newton interior--point algorithm with a line search strategy based on the Eisenstat and Walker rule.
       - standard C++
       - partial AMPL interface
       - HP Itanium2 workstation.

  • A Collection of optimal control problems [Last updated: December 2006]

    Authors: S. Bonettini, V. Ruggiero

    Topic: A collection of 25 nonlinear and quadratic programming problems arising from elliptic and parabolic control problems.

    Description: For each problem it is available the AMPL model; a detailed description of the discretization technique and of the structure of the Jacobian and Hessian matrices can be found in the documentation.

  • VIsemiLSQRnew2 [Last updated: December 2006]

    Authors: V. Ruggiero, F. Tinti

    Topic: A Fortran 90 software designed to solve large scale variational inequality problems using the generalisation of the Inexact Newton method applied to a semismooth nonlinear system..

    Description: Semismooth algorithm with a line search strategy. We have used LSQR method, combined by a convenient preconditioner (a variant of Incomplete LU-factorization). Furthemore we have introduced an adaptive stopping rule. Code:
       - Fortran 90
       - partial AMPL interface
    Tested platform
       - DEC ALPHA 21264 EV6/7 633Mhz workstation


Upcoming software

  • A Parallel Matlab Linux cluster-enabled tool for Dynamic Magnetic Resonance Imaging

    Authors: G. Landi, E. Loli Piccolomini, F. Zama

    Topic: A parallel Matlab-based software, implementing a domain decomposition technique, for dynamic Magnetic Resonance (MR) sequences reconstruction. The software is designed for MPI-based PC Linux clusters running open source software for the network.


Status: completed.

 Last updated: 15/3/2007.