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Transformation of quadratic forms to perfect squares for broken extremals

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

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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