Geodesic
On the regularized Lagrange principle in the iterative form and its application for solving unstable problems
Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 3-18

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For a convex programming problem in a Hilbert space with an operator equality constraints the resistant to input data errors Lagrange principle in sequential non-differential form or, in other words, the regularized Lagrange principle in iterative form is proved. The possibility of the applicability of it for direct solving of unstable inverse problems is discussed. As an example of such problem we consider the problem of finding the normal solution of the Fredholm integral equation of the 1st kind. The results of numerical calculations are shown.
Keywords: Lagrange principle, Kuhn-Tucker theorem, instability, sequential optimization, duality, dual regularization, iterative algorithm, solving unstable problems. 
@article{MM_2016_28_11_a0,
     author = {F. A. Kuterin and M. I. Sumin},
     title = {On the regularized {Lagrange} principle in the iterative form and its application for solving unstable problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {28},
     number = {11},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_11_a0/}
}
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F. A. Kuterin; M. I. Sumin. On the regularized Lagrange principle in the iterative form and its application for solving unstable problems. Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 3-18. http://geodesic.mathdoc.fr/item/MM_2016_28_11_a0/