Experience in organizing hybrid parallel calculations in the Evtushenko-Golikov method for problems with block-angular structure / Popov L.D. // Automation and Remote Control. - 2014. - V. 75, l. 4. - P. 622-631.

ISSN:
00051179
Type:
Article
Abstract:
The potentialities of hybrid parallelization of the Evtushenko-Golikov method where the philosophy of the modified Lagrange functions is merged with the Mangasarian-Kanzow technology of quadratic approximation were demonstrated for the high-dimension linear programming problems with the block-diagonal matrix of constraints and horizontal bordering. © 2014 Pleiades Publishing, Ltd.
Author keywords:
Index keywords:
Automation; Block diagonal matrices; Block-angular structure; High dimensions; Hybrid parallelization; Lagrange functions; Linear programming problem; Parallel calculation; Quadratic approximation; Co
DOI:
10.1134/S0005117914040031
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84899552908&doi=10.1134%2fS0005117914040031&partnerID=40&md5=b3c6c34771221cf2c30c84301a88dec4
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Affiliations Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
References Eremin, I.I., (1998) Teoriya Lineinoi Optimizatsii, , Ross. Akad. Nauk Yekaterinburg (Theory of Linear Optimization); Vasil'Ev, F.P., Ivanitskii, A., (2003) Lineinoe Programmirovanie, , Faktorial Moscow (Linear Programming); Minoux, M., (1983) Programmation Mathématique. Théorie et Algorithmes, , Dunod Paris 0546.90056 Translated under the title Matematicheskoe programmirovanie, Moscow: Nauka, 1990; Lasdon, L.S., (1969) Optimization Theory for Large Systems, , Macmillan London Translated under the title Optimizatsiya bol'shikh sistem, Moscow: Nauka, 1975; Polyak, B.T., Tret'Yakov, N.V., On One Iterative Method of Linear Programming and Its Economic Interpretation (1972) Ekon. Mat. Metody, 8 (5), pp. 740-751; Golikov, A.I., Evtushenko, Y., Mollaverdi, N., Using the Newton Method in Solution of the Linear Programming Problems of High Dimensionality (2004) Zh. Vychisl. Mat. Mat. Fiz., 44 (9), pp. 1564-1573. , 1136.90392 2238180; Garanzha, V.A., Golikov, A.I., Evtushenko, Y., Parallel Realization of the Newton Method to Solve Large Problems of Linear Programming (2009) Zh. Vychisl. Mat. Mat. Fiz., 49 (8), pp. 1369-1384. , 1183.90297 2603145; Popov, L.D., Quadratic Approximation of the Penalty Functions in the Linear Programming Problems of High Dimensionality (2007) Zh. Vychisl. Mat. Mat. Fiz., 47 (2), pp. 206-221. , 1210.49034 2351812; Mangasarian, O.L., A Finite Newton Method for Classification (2002) Optimizat. Meth. Software, 17, pp. 913-930. , 10.1080/1055678021000028375 1065.90078 1953825; Kanzow, C., Qi, H., Qi, L., On the Minimum Norm Solution of Linear Program (2003) J. Optimiz. Theory Appl., 116, pp. 333-345. , 10.1023/A:1022457904979 1043.90046 1967673; Ortega, J.M., (1989) Introduction to Parallel and Vector Solution of Linear Systems, , Plenum New York Translated under the title Vvedenie v parallel'nye i vektornye metody resheniya lineinykh sistem, Moscow: Mir, 1991; Golub, G., Van Loan, C., (1989) Matrix Computations, , John Hopkins Univ. Press Baltimor 0733.65016 Translated under the title Matrichnye vychisleniya, Moscow: Mir, 1999, 2nd ed
Correspondence Address Popov, L.D.; Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation; email: popld@imm.uran.ru
Publisher Maik Nauka Publishing / Springer SBM
Language of Original Document English
Abbreviated Source Title Autom. Remote Control
Source Scopus