Why regularization of Lagrange principle and Pontryagin maximum principle is needed and what it gives
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 757-775 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the regularization of the classical Lagrange principle and the Pontryagin maximum principle in convex problems of mathematical programming and optimal control. On example of the “simplest” problems of constrained infinitedimensional optimization, two main questions are discussed: why is regularization of the classical optimality conditions necessary and what does it give?
Keywords: convex programming, dual regularization, regularized Lagrange principles, optimal control, inverse problem, regularized iterative Pontryagin maximum principle.
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M. I. Sumin. Why regularization of Lagrange principle and Pontryagin maximum principle is needed and what it gives. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 757-775. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a19/

[1] F. P. Vasilev, Metody optimizatsii, Izd-vo MTsNMO, M., 2011, 433 pp. (In Russian)

[2] M. I. Sumin, “Regularized parametric Kuhn-Tucker theorem in a Hilbert space”, Computational Mathematics and Mathematical Physics, 51:9 (2011), 1594–1615 (In Russian)

[3] M. I. Sumin, “Stable sequential convex programming in a Hilbert space and its application for solving unstable problems”, Computational Mathematics and Mathematical Physics, 54:1 (2014), 25–49 (In Russian)

[4] V. A Trenogin, Functional Analysis, Nauka Publ., Moscow, 1980, 496 pp. (In Russian)

[5] Functional Analysis, eds. S. G Krein, Nauka Publ., Moscow, 1972, 544 pp. (In Russian)

[6] V. I. Plotnikov, “The convergence of finite-dimensional approximations (in the problem of the optimal heating of an inhomogeneous body of arbitrary shape”, Computational Mathematics and Mathematical Physics, 8:1 (1968), 136–157 (In Russian)

[7] V. I. Plotnikov, “An energy inequality and the overdeterminacy property of a system of eigenfunctions”, Mathematics of the USSR – Izvestiya, 32:4 (1968), 743–755 (In Russian)

[8] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Nauka Publ., Moscow, 1967, 736 pp. (In Russian)

[9] M. I. Sumin, “A regularized gradient dual method for the inverse problem of a final observation for a parabolic equation”, Computational Mathematics and Mathematical Physics, 44:11 (2004), 2001–2019 (In Russian)

[10] M. I. Sumin, “Duality-based regularization in a linear convex mathematical programming problem”, Computational Mathematics and Mathematical Physics, 47:4 (2007), 602–625 (In Russian)

[11] M. I. Sumin, “Parametric dual regularization in optimization, optimal control and inverse problems”, Tambov University Reports. Series: Natural and Technical Sciences, 15:1 (2010), 467–492 (In Russian)

[12] F. A. Kuterin, M. I. Sumin, “The regularized iterative Pontryagin maximum principle in optimal control. I. Optimization of a lumped system”, The Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 26:4 (2016), 474–489 (In Russian)

[13] F. A. Kuterin, M. I. Sumin, “The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system”, The Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 27:1 (2017), 26–41 (In Russian)

[14] F. A. Kuterin, M. I. Sumin, “On the regularized Lagrange principle in the iterative form and its application for solving unstable problems”, Mathematical Models and Computer Simulations, 28:11 (2016), 3–18 (In Russian)

[15] F. A. Kuterin, M. I. Sumin, “Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems”, Computational Mathematics and Mathematical Physics, 57:1 (2017), 55–68 (In Russian)

[16] A. V. Kalinin, M. I. Sumin, A. A. Tyukhtina, “Stable sequential Lagrange principles in the inverse final observation problem for the system of Maxwell equations in the quasistationary magnetic approximation”, Differential Equations, 52:5 (2016), 608–624 (In Russian)

[17] A. V. Kalinin, M. I. Sumin, A. A. Tyukhtina, “Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential lagrange principles for their solving”, Computational Mathematics and Mathematical Physics, 57:2 (2017), 187–209 (In Russian)

[18] M. I. Sumin, Ill-Posed Problems and their Solutions, N. I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 2009, 289 pp. (In Russian)

[19] J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972, 531 pp.