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On the regularized Lagrange principle in iterative form and its application for solving unstable problems

Autor: M. I. Sumin, F. A. Kuterin

Publikováno v: Mathematical Models and Computer Simulations. 9:328-338

For a convex programming problem in a Hilbert space with operator equality constraints, the Lagrange principle in sequential nondifferential form or, in other words, the regularized Lagrange principle in iterative form, that is resistant to input dat

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e315f9c1f7ad6a52c2cbe0786a5411a1
https://doi.org/10.1134/s2070048217030085

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Inverse final observation problems for Maxwell’s equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving

Autor: M. I. Sumin, A. A. Tyukhtina, A. V. Kalinin

Publikováno v: Computational Mathematics and Mathematical Physics. 57:189-210

An initial–boundary value problem for Maxwell’s equations in the quasi-stationary magnetic approximation is investigated. Special gauge conditions are presented that make it possible to state the problem of independently determining the vector ma

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::af80bc2b1a8bda47767ebda7c88c2790
https://doi.org/10.1134/s0965542517020075

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Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems

Autor: F. A. Kuterin, M. I. Sumin

Publikováno v: Computational Mathematics and Mathematical Physics. 57:71-82

A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ce8354efd3cde2920606f615d9597274
https://doi.org/10.1134/s0965542517010092

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Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

Autor: M. I. Sumin

Publikováno v: Computational Mathematics and Mathematical Physics. 55:935-961

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiabil

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::aee07616e4f04581d73bc266cefa0667
https://doi.org/10.1134/s0965542515060111

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The stable Lagrange principle in sequential form for the convex programming problem in a uniformly convex space and its applications

Autor: M. I. Sumin, A. A. Gorshkov

Publikováno v: Russian Mathematics. 59:11-23

We consider the convex programming problem in a reflexive space with operator equality constraint and finite number of functional inequality constraints. For this problem we prove the stable with respect to the errors in the initial data Lagrange pri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6f21ac8b17674502fe7b25e24f471689
https://doi.org/10.3103/s1066369x15010028

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Stable sequential convex programming in a Hilbert space and its application for solving unstable problems

Autor: M. I. Sumin

Publikováno v: Computational Mathematics and Mathematical Physics. 54:22-44

A parametric convex programming problem with an operator equality constraint and a finite set of functional inequality constraints is considered in a Hilbert space. The instability of this problem and, as a consequence, the instability of the classic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b39b72f547a42d133381abf4ba9aa452
https://doi.org/10.1134/s0965542514010138

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Sequential stable Kuhn-Tucker theorem in nonlinear programming

Autor: A. V. Kanatov, M. I. Sumin

Publikováno v: Computational Mathematics and Mathematical Physics. 53:1078-1098

A general parametric nonlinear mathematical programming problem with an operator equality constraint and a finite number of functional inequality constraints is considered in a Hilbert space. Elements of a minimizing sequence for this problem are for

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c82e490c08e1664192202f352371a49f
https://doi.org/10.1134/s0965542513080083

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Dual regularization and Pontryagin’s maximum principle in a problem of optimal boundary control for a parabolic equation with nondifferentiable functionals

Autor: M. I. Sumin

Publikováno v: Proceedings of the Steklov Institute of Mathematics. 275:161-177

A problem of optimal boundary control is considered for a divergent linear parabolic equation. Equality constraints of the problem are given by nondifferentiable functionals. A dual regularization algorithm stable to errors in initial data is constru

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b5b038f114f678cc570d544ec4119743
https://doi.org/10.1134/s0081543811090124

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