|
|
|
|
ЛИТЕРАТУРА
|
|
| |
| 1. |
Gurobi optimizer reference manual, Gurobi Optimization, Beaverton, 2021 www.gurobi.com/documentation/9.5/refman/index.html (accessed Feb. 27, 2022) |
| 2. |
IBM ILOG CPLEX Optimizer, IBM, Armonk, 2022 www.ibm.com/analytics/cplex-optimizer (accessed Feb. 27, 2022) |
| 3. |
Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D., LAPACK users' guide, SIAM, Philadelphia, 1999, 404 pp.  |
| 4. |
SuiteSparse: A suite of sparse matrix software, Texas A&M Univ, College Station, 2022 people.engr.tamu.edu/davis/suitesparse.html (accessed Feb. 27, 2022) |
| 5. |
Dantzig G. B., Wolfe Ph., “The decomposition algorithm for linear programming”, Econometrica, 9:4 (1961), 767–778  |
| 6. |
AMPL homepage, ampl.com, AMPL Optimization, Mountain View, CA (accessed Feb. 27, 2022) |
| 7. |
Fourer R., Gay D. M., Kernighan B. W., AMPL: A modeling language for mathematical programming, Cengage Learning, Boston, 2003, 517 pp. |
| 8. |
GAMS — A user's guide, GAMS Software, Frechen, 2022 www.gams.com/35/docs/UG_MAIN.html (accessed Feb. 27, 2022) |
| 9. |
GLPK (GNU linear programming kit), Free Software Found., Boston, MA, 2012 www.gnu.org/software/glpk/ (accessed Feb. 27, 2022) |
| 10. |
NEOS Server, Univ. Wisconsin, Madison, WI, 2022 neos-server.org/neos/ (accessed Feb. 27, 2022) |
| 11. |
Kahan G., “Walking through a columnar approach to linear programming of a business”, Interfaces, 12:3 (1982), 32–39 |
| 12. |
Nurminski E. A., “Single-projection procedure for linear optimization”, J. Glob. Optim., 66:1 (2016), 95–110   |
| 13. |
Goldman A. J., Tucker A. W., “Theory of linear programming”, Linear inequalities and related systems, Annals of Mathematics Studies, 38, Princeton Univ. Press, Princeton, NJ, 1956, 53–97 |
| 14. |
Von Neumann J., “On rings of operators. Reduction theory”, Ann. Math., 50:2 (1949), 401–485 |
| 15. |
Bauschke H. H., Borwein J. M., “On the convergence of von Neumann's alternating projection algorithm for two sets”, Set-Valued Anal., 1993, no. 1, 185–212 |
| 16. |
Escalante R., Raydan M., Alternating projection methods, SIAM, Philadelphia, 2011 |
| 17. |
C. Michelot, “A finite algorithm for finding the projection of a point onto the canonical simplex of $E^n$”, J. Optim. Theory Appl., 50:1 (1986), 195–200 |
| 18. |
Малоземов В. Н., Тамасян Г. Ш., “Два быстрых алгоритма проектирования точки на стандартный симплекс”, Журн. вычисл. математики и мат. физики, 56:5 (2016), 742–755  ; V. N. Malozemov and G. Sh. Tamasyan, “Two fast algorithms for projecting a point onto the canonical simplex”, Comput. Math. Math. Phys., 56:5 (2016), 730–743 |
| 19. |
Нурминский Е. А., “Проекция на внешне заданные полиэдры”, Журн. вычисл. математики и мат. физики, 48:3 (2008), 387–396 ; E. A. Nurminski, “Projection onto polyhedra in outer representation”, Comput. Math. Math. Phys., 48:3 (2008), 367–375 |
| 20. |
Nurminski E. A., Shamray N. B., “Row-oriented decomposition in large-scale linear optimization”, Optimization and Applications, Proc. Int. Conf. OPTIMA 2021 (Petrovac, Montenegro, Sep. 27–Oct. 1, 2021), Lect. Notes Comput. Sci., 13078, Springer, Heidelberg, 2021, 50–63 |
| 21. |
Greenberg H. J., Lundgren J. R., Maybee J. S., “Graph theoretic methods for the qualitative analysis of rectangular matrices”, SIAM J. Algebraic Discrete Methods, 2:3 (1981), 227–239 |
