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@article{492729, author = {Hilscher, Roman and Zeidan, Vera}, article_location = {Berlin}, article_number = {1}, keywords = {Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Conjugate interval; Conjoined basis; Riccati difference equation; Discrete Jacobi condition}, language = {eng}, issn = {0025-584X}, journal = {Mathematische Nachrichten}, title = {Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control}, volume = {266}, year = {2004} }
TY - JOUR ID - 492729 AU - Hilscher, Roman - Zeidan, Vera PY - 2004 TI - Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control JF - Mathematische Nachrichten VL - 266 IS - 1 SP - 48-59 EP - 48-59 PB - WILEY-VCH Verlag SN - 0025584X KW - Discrete quadratic functional KW - Nonnegativity KW - Positivity KW - Linear Hamiltonian difference system KW - Conjugate interval KW - Conjoined basis KW - Riccati difference equation KW - Discrete Jacobi condition N2 - In this paper we provide a characterization of the nonnegativity of a discrete quadratic functional I with fixed right endpoint in the optimal control setting. This characterization is closely related to the kernel condition earlier introduced by M.Bohner as a part of a focal points definition for conjoined bases of the associated linear Hamiltonian difference system. When this kernel condition is satisfied only up to a certain critical index m, the traditional conditions, which are the focal points, conjugate intervals, implicit Riccati equation, and partial quadratic functionals, must be replaced by a new condition. This new condition is determined to be the nonnegativity of a block tridiagonal matrix, representing the remainder of I after the index m, on a suitable subspace. ER -
HILSCHER, Roman a Vera ZEIDAN. Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. \textit{Mathematische Nachrichten}. Berlin: WILEY-VCH Verlag, 2004, roč.~266, č.~1, s.~48-59. ISSN~0025-584X.
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