Transformation of quadratic forms to perfect squares for broken extremals

N. P. Osmolovskii, F. Lempio: Transformation of quadratic forms to perfect squares for broken extremals
Set-Valued Analysis 10 (2-3), 209 - 232, 2002

DOI: 10.1023/A:1016588116615
MR Nummer: 1926381
Zentralblattnummer: 1050.49016
Keywords: broken extremals, perfect squares, Riccati equation, sufficient optimality conditions.
Mathematics Subject Classification Code: 49K15


Abstract:

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.

Contents:

1. Introduction
2. The Simplest Problem of the Calculus of Variations
3. General Problem of the Calculus of Variations

Chair -

|  University of Bayreuth -