Download PDF - P-order necessary and sufficient conditions for optimality in singular calculus of variationsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

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

Authors 1, 1, 2, 3

Affiliations

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

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.

Keywords

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

Bibliography

  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)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2010/30/2
Export to PBN, Opens in new tab
Pages:
269-279
Main language of publication
English
Received
2009-10-06
Published
2010

DOI: 10.7151/dmdico.1124

Exact and natural sciences