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

Agnieszka Prusińska; Alexey Tret'yakov

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

- Volume: 30, Issue: 2, page 269-279
- ISSN: 1509-9407

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topAgnieszka Prusińska, and Alexey Tret'yakov. "P-order necessary and sufficient conditions for optimality in singular calculus of variations." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.2 (2010): 269-279. <http://eudml.org/doc/271182>.

@article{AgnieszkaPrusińska2010,

abstract = {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.},

author = {Agnieszka Prusińska, Alexey Tret'yakov},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {singular variational problem; necessary condition of optimality; p-regularity; p-factor operator; -regularity; -factor operator},

language = {eng},

number = {2},

pages = {269-279},

title = {P-order necessary and sufficient conditions for optimality in singular calculus of variations},

url = {http://eudml.org/doc/271182},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Agnieszka Prusińska

AU - Alexey Tret'yakov

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

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2010

VL - 30

IS - 2

SP - 269

EP - 279

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/271182

ER -

## References

top- [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 Zbl1037.49025
- [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)