## Title data

Osmolovskii, Nikolai P. ; Lempio, Frank:

**Transformation of quadratic forms to perfect squares for broken extremals.**

*In:* Set-Valued Analysis.
Vol. 10
(2002)
Issue 2/3
.
- pp. 209-232.

ISSN 0927-6947

DOI: https://doi.org/10.1023/A:1016588116615

Review: |

## Abstract in another language

In this paper we study a quadratic form which corresponds to an extremal with piecewise continuous control in variational problems. This form, compared with the classical one, has some new terms connected with the set Θ of all points of discontinuity of the control. Its positive definiteness is a sufficient optimality condition for broken extremals. We show that if there exists a solution to corresponding Riccati equation satisfying some jump condition at each point of the set Θ, then the quadratic form can be transformed to a perfect square, just as in the classical case. As a result we obtain sufficient conditions for positive definiteness of the quadratic form in terms of the Riccati equation and hence, sufficient optimality conditions for broken extremals.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Broken extremals; Perfect squares; Riccati equation; Sufficient optimality conditions |

Subject classification: | Mathematics Subject Classification Code: 49K15 |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 01 Mar 2021 14:43 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63407 |