naa a22 4500 510811485 CHVBK 20180411083444.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1134/S0081543813090058 doi (NATIONALLICENCE)springer-10.1134/S0081543813090058 Interior penalty functions and duality in linear programming [Elektronische Daten] [I. Eremin, L. Popov] Logarithmic additive terms of barrier type with a penalty parameter are included in the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problems are formulated. Pleiades Publishing, Ltd., 2013 linear programming nationallicence duality nationallicence inner penalty functions nationallicence Eremin I. aut Popov L. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283(2013-12-01), 56-63 0081-5438 283<56 2013 283 11501 https://doi.org/10.1134/S0081543813090058 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813090058 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Eremin I. aut NATIONALLICENCE 700 1- Popov L. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283(2013-12-01), 56-63 0081-5438 283<56 2013 283 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer