Software
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:
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.: 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).
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.
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
the file contains the source of a program that generates a sparse linearly constrained convex QP problems with assigned features;
the file contains an example of input data that must be suppied by the user for the program test98.f;
the file shows the results obtained by the program test98.f when the user supplies as input data the values in the file inputtest98;
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;
the file contains an example of input data that must be suppied by the user for the program pm_sm.f;
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;
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);
the file contains an example of input data that must be suppied by the user for the program mpm.f;
the file shows the results obtained by the program mpm.f when the user supplies as input data the values in the file inputmpm;
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);
the file contains an example of input data that must be suppied by the user for the program fpm_asm.f;
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;
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)) ;
the file contains an example of input data that must be suppied by the user for the program afpm.f;
the file shows the results obtained by the program afpm.f when the user supplies as input data the values in the file inputafpm;
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;
the file contains an example of input data that must be suppied by the user for the program vpm.f;
the file shows the results obtained by the program vpm.f when the user supplies as input data the values in the file inputvpm;
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;
the file contains an example of input data that must be suppied by the user for the program avpm.f;
the file shows the results obtained by the program vpm.f when the user supplies as input data the values in the file inputavpm;
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;
the file contains an example of input data that must be suppied by the user for the program nag_test.f;
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.
