Software for the Numerical Evaluation of

Software for the Numerical Evaluation of Projection-Type Methods for Large Quadratic Programs

This repository of software contains a set of programs for the numerical evaluation of the Projection-Type methods for large and sparse convex quadratic programs of the form:

minimize ½ x^T G x + q^T x subject to C x = d A x ³ b

The results of a numerical experimentation obtained by these programs on a set of test problems are reported in the following monograph:

V. Ruggiero, E. Galligani, L. Zanni - Projection-Type Methods for Large Convex Quadratic Programs: Theory and Computational Experience. Progetto MURST: "Analisi Numerica: Metodi e Software Matematico", Monografia n. 5, Ferrara (2000).

This monograph collects the results of the following scientific papers, supported by the MURST Project Numerical Analysis: Methods and Mathematical Software , in the years 1998-2000:

Galligani E., Ruggiero V., Zanni L.: Parallel solution of large scale quadratic programs - High Performance Algorithms and Software in Nonlinear Optimization (R. De Leone, A. Murli, P. Pardalos, G. Toraldo eds.) Kluwer Academic Publ. (1998).
Ruggiero V., Zanni L.: On a Class of Iterative Methods for Large--Scale Convex Quadratic Programs - Numerical Methods in Optimization (A. Maugeri and E. Galligani, eds) Rend. Circ. Matem. Palermo, Ser. II, Suppl. 58 , (1999) 213-227.
Ruggiero V., Zanni L.: A modified projection algorithm for large strictly convex quadratic programs – Journal of Optimization Theory and Applications, 104, n. 2, 2000.
Ruggiero V., Zanni L.: On the efficiency of splitting and projection methods for large strictly convex quadratic programs – Nonlinear Optimization and Related Topics (G. Di Pillo, F. Giannessi eds.), Kluwer Academic Publishers, (2000).
Ruggiero V., Zanni L.: An overview on projection-type methods for convex large-scale quadratic programs - Equilibrium Problems and Variational Models (A. Maugeri, F. Giannessi, P. Pardalos eds.), Kluwer Academic Press (2000).
Ruggiero V., Zanni L.: Variable projection methods for large convex quadratic programs - Recent Trend in Numerical Analysis (L. Brugnano, D. Trigiante eds.), Advances in Computation Theory and Practice, Nova Science Book and Journals, Huntington, NJ (2000).

The test problems used in this experimentation are generated by a random generator described in the following monograph:

C. Durazzi, V. Ruggiero, L. Zanni - A Random Generator for Random Large-Scale Linearly Constrained Quadratic Programming Test Problems. Progetto MURST: "Analisi Numerica: Metodi e Software Matematico", Monografia n. 6, Ferrara (2000).

All the programs are written in Fortran 77 for a Digital Alpha workstation with Unix operating system. An exhaustive documentation of each program is reported in the comments of the source file.

Each program can be execute by the following commands:

>f90 -o test98.x test98.f -ldxml (or f77 -o test98.x test98.f -ldxml)

>test98<inputtest98>outputtest98

The unformatted files data.dat and constr.dat are generated.

>f90 -o vpm.x vpm.f -ldxml (or f99 -o vpm.x vpm.f -ldxml)

>vpm<inputvpm

The output file vpm.dat is produced.

The Fortran program nag_test.f uses the Fortran 77 NAG library:

>f77 -o nag_test.x nag_test.f -lnag

>nag_test.x<inputnag_test

The output file nag.dat is produced.

CONTENTS OF THE REPOSITORY

test98.f

the file contains the source of a program that generates a sparse linearly constrained convex QP problems with assigned features;

inputtest98

the file contains an example of input data that must be suppied by the user for the program test98.f;

outputtest98

the file shows the results obtained by the program test98.f when the user supplies as input data the values in the file inputtest98;

pm_sm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the classical projection method or by the classical splitting method;

inputpm_sm

the file contains an example of input data that must be suppied by the user for the program pm_sm.f;

pm_sm.dat

the file shows the results obtained by the program pm_sm.f when the user supplies as input data the values in the file inputpm_sm;

mpm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the modified projection method of Solodov and Tseng (M.V. Solodov - P.Tseng: Modified Projection-Type Methods for Monotone Variational Inequalities, SIAM J. Control Optim., 34, (1996), 1814-1830);

inputmpm

the file contains an example of input data that must be suppied by the user for the program mpm.f;

mpm.dat

the file shows the results obtained by the program mpm.f when the user supplies as input data the values in the file inputmpm;

fpm_asm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the scaled gradient projection method with a limited minimization rule (D.P. Bertsekas: Nonlinear Programming, Athena Scientific (1995)) or by the accelerated splitting method ( E. Galligani, V. Ruggiero, L. Zanni: Splitting Methods for Constrained Quadratic Programs in Data Analysis, Computers Math. Applic., 32 (1996), 1-9);

inputfpm_asm

the file contains an example of input data that must be suppied by the user for the program fpm_asm.f;

fpm_asm.dat

the file shows the results obtained by the program fpm_asm.f when the user supplies as input data the values in the file inputfpm_asm;

afpm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the scaled gradient projection method with an Armijo rule along a projection arc (D.P. Bertsekas: Nonlinear Programming, Athena Scientific (1995)) ;

inputafpm

the file contains an example of input data that must be suppied by the user for the program afpm.f;

afpm.dat

the file shows the results obtained by the program afpm.f when the user supplies as input data the values in the file inputafpm;

vpm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the variable projection method;

inputvpm

the file contains an example of input data that must be suppied by the user for the program vpm.f;

vpm.dat

the file shows the results obtained by the program vpm.f when the user supplies as input data the values in the file inputvpm;

avpm.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the adaptive variable projection method;

inputavpm

the file contains an example of input data that must be suppied by the user for the program avpm.f;

avpm.dat

the file shows the results obtained by the program vpm.f when the user supplies as input data the values in the file inputavpm;

nag_test.f

the file contains the source of a program that computes a numerical solution of a sparse linearly constrained convex QP problems by the NAG routine E04NKF;

inputnag

the file contains an example of input data that must be suppied by the user for the program nag_test.f;

nag.dat

the file shows the results obtained by the program nag_test.f when the user supplies as input data the values in the file inputnag.