Pacific national university Main page Bulletin of Pacific national university

UDC 519.68

© Namm R. V., Tkachenko A. S., 2007

Solving Sinorini half coercively scalar task by Udzava method

The methods of solving variational inequalities in mechanical engineering that are based on the searching of saddle points of the Lagrange functional are supposed to have positive determinacy of the corresponding bilinear forms. The convergence of the methods is provided with the coordination of a positive constant of determinacy with shifts parameter on a dual variable. Therefore the algorithms of the searching of saddle points that are based on the classical Lagrange functional are unfit for half coercively varitional inequalities. To complete this blank simultaneously with classical Lagrange functional its modified analogue is examined in the given work.

References:

  1. Reshenie variatsionnykh neravenstv v mekhanike / I. Glavachek, YA. Gaslinger, I. Nechas, YA. Lovishek. M., 1986.
  2. Dyuvo G., Lions ZH.-L.  Neravenstva v fizike i mekhanike. M., 1980.
  3. Chislennoe issledovanie variatsionnykh neravenstv / Glovinski R., Lions ZH.-L., Tremol`er R. M., 1979.
  4. Numerical methods for nonlinear variational problems. R. Glowinski. New York, 1984.
  5. Vu G., Namm R. V., Sachkov S. A. Iteratsionnyy metod poiska sedlovoy tochki dlya polukoertsitivnoy zadachi Sin`orini, osnovannyy na modifitsirovannom funktsionale Lagranzha // ZH. vychisl. matem. i matem. fiz. 2006. T. 46. ¹ 1.
  6. Metod iterativnoy proksimal`noy regulyarizatsii dlya  poiska sedlovoy tochki v polukoertsitivnoy zadache Sin`orini / G. Vu, S. Kim, R. V. Namm., S. A. Sachkov. // ZH. vychisl. matem. i matem. fiz. 2006. T. 46. ¹ 11.
  7. Namm R. V. O skorosti skhodimosti metoda konechnykh elementov v zadache Sin`orini // Differentsial`nye uravneniya. 1995. T. 31. ¹ 5.
  8. Stable methods for ill-posed variational inequalities in mechanics. R. V. Namm. Berlin. Springer: Lecture Notes in Economics and Mathematical Systems. 1997. V. 452.
  9. Namm R. V. Vvedenie v teoriyu i metody resheniya variatsionnykh neravenstv. Habarovsk, 1999.
  10. Grossman K., Kaplan A. A. Nelineynoe programmirovanie na osnove bezuslovnoy minimizatsii. Novosibirsk, 1981.
  11. Gol`shteyn E. G., Tret`yakov N. V. Modifitsirovannye funktsii Lagranzha. M., 1989.

Download Download article (335.8 Kb)

Сontents Сontents