P-order necessary and sufficient conditions for optimality in singular calculus of variations

• Autorzy: Agnieszka Prusińska , Alexey Tret'yakov
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.

Słowa kluczowe

EN

singular variational problem; necessary condition of optimality; p-regularity; p-factor operator

Kategorie tematyczne

• 49N60: Regularity of solutions
• 90C30: Nonlinear programming
• 46N10: Applications in optimization, convex analysis, mathematical programming, economics
• 49K27: Problems in abstract spaces

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 269-279

Daty

wydano

2010

otrzymano

2009-10-06

Twórcy

autor

Agnieszka Prusińska

• Institute of Mathematics and Physics, University of Podlasie, Poland

autor

Alexey Tret'yakov

• Institute of Mathematics and Physics, University of Podlasie, Poland
• System Research Institute, Polish Academy of Sciences, Warsaw, Poland
• Dorodnicyn Computing Center, Moscow, Russia

Bibliografia

• [1] V.M. Alexeev, V.M. Tihomirov and S.V. Fomin, Optimal Control, (Consultants Bureau, New York, 1987). Translated from Russian by V.M. Volosov.
• [2] O.A. Brezhneva and A.A. Tret'yakov, Optimality conditions for degenerate extremum problems with equality constraints, SIAM J. Contr. Optim. 42 (2003), 729-745. doi: 10.1137/S0363012901388488
• [3] A.F. Izmailov and A.A. Tret'yakov, Factor-Analysis of Non-Linear Mapping (Nauka, Moscow, Fizmatlit Publishing Company, 1994).
• [4] K.N. Belash and A.A. Tret'yakov, Methods for solving degenerate problems, USSR Comput. Math. and Math. Phys. 28 (1988), 90-94. doi: 10.1016/0041-5553(88)90116-4
• [5] A.A. Tret'yakov, Necessary and Sufficient Conditions for Optimality of p-th Order, USSR Comput. Math. and Math. Phys. 24 (1984), 123-127. doi: 10.1016/0041-5553(84)90132-0
• [6] J. Glazunov, Variational methods for solving differential equations, Wydawnictwo Politechniki Gdańskiej, Gdańsk 2000 (in Polish)

Identyfikatory

DOI

10.7151/dmdico.1124