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ON STABLE LAGRANGE PRINCIPLE IN ITERATIVE FORM IN CONVEX PROGRAMMING AND ITS APPLICATION FOR SOLVING UNSTABLE OPERATOR EQUATIONS OF THE FIRST KIND

Annotation

The stable Lagrange principle in iterative form for the convex optimization problem and its application for solving unstable equations of the first kind are discussed. The results of numerical solving of Fredholm integral equation based on it are provided.

Keywords

Lagrange principle; instability; sequential optimization; dual regularization; iterative algorithm

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UDC

519.853.3+517.983.54

Pages

1239-1246

References

1. Tihonov A.N., Arsenin V.Ja. Metody reshenija nekorrektnyh zadach. M.: Nauka, 1986. 2. Sumin M.I. Reguljarizacija v linejno vypukloj zadache matematicheskogo programmirovanija na osnove teorii dvojstvennosti // Zhurn. vychisl. matem. i matem. fiz. 2007. T. 47. № 4. S. 602–625. 3. Sumin M.I. Ustojchivoe sekvencial'noe vypukloe programmirovanie v gil'bertovom prostranstve i ego prilozhenie k resheniju neustojchivyh zadach // Zhurn. vychisl. matem. i matem. fiz. 2014. T. 54. № 1. S. 25–49. 4. Sumin M.I. Reguljarizovannaja parametricheskaja teorema Kuna–Takkera v gil'bertovom prostranstve // Zhurn. vychisl. matem. i matem. fiz. 2011. T. 51. № 9. S. 1594–1615. 5. Sumin M.I. On the Stable Sequential Kuhn–Tucker Theorem and its Applications // Applied Mathematics. 2012. V. 3. No. 10A (Special issue “Optimization”). P. 1334–1350. 6. Jerrou K.Dzh., Gurvic L., Udzava H. Issledovanija po linejnomu i nelinejnomu programmirovaniju. M.: IL, 1962. 7. Minu M. Matematicheskoe programmirovanie. Teorija i algoritmy. M.: Nauka, 1990. 8. Sumin M.I. Iterativnaja reguljarizacija gradientnogo dvojstvennogo metoda dlja reshenija uravnenija Fredgol'ma pervogo roda // Vestnik Nizhegorodskogo universiteta. Serija Matematika. Vyp. 2. 2004. S. 193–209.

Received

2015-04-24

Section of issue

Scientific articles

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