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Full-Text Articles in Physical Sciences and Mathematics
On The Lqg Theory With Bounded Control, D. V. Iourtchenko, J. L. Menaldi, A. S. Bratus
On The Lqg Theory With Bounded Control, D. V. Iourtchenko, J. L. Menaldi, A. S. Bratus
Mathematics Faculty Research Publications
We consider a stochastic optimal control problem in the whole space, where the corresponding HJB equation is degenerate, with a quadratic running cost and coeffcients with linear growth. In this paper we provide a full mathematical details on the key estimate relating the asymptotic behavior of the solution as the space variable goes to infinite.
Generalized Newton's Method Based On Graphical Derivatives, T Hoheisel, C Kanzow, Boris S. Mordukhovich, Hung M. Phan
Generalized Newton's Method Based On Graphical Derivatives, T Hoheisel, C Kanzow, Boris S. Mordukhovich, Hung M. Phan
Mathematics Research Reports
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper …