"DE - Spolkov\u00E1 republika N\u011Bmecko" . . . . "\u0160imon Hilscher, Roman" . . . "RIV/00216224:14310/04:00011373!RIV09-GA0-14310___" . . "V tomto \u010Dl\u00E1nku popisujeme charakterizaci nez\u00E1pornosti diskr\u00E9tn\u00EDho kvadratick\u00E9ho funkcion\u00E1lu I s pevn\u00FDm prav\u00FDm koncem v diskr\u00E9tn\u00EDm optim\u00E1ln\u00EDm \u0159\u00EDzen\u00ED. Tato charakterizace je \u00FAzce spjata s podm\u00EDnkou na j\u00E1dro hlavn\u00EDho \u0159e\u0161en\u00ED p\u0159\u00EDslu\u0161n\u00E9ho line\u00E1rn\u00EDho Hamiltonovsk\u00E9ho diferen\u010Dn\u00EDho syst\u00E9mu, kterou ji\u017E d\u0159\u00EDve odvodil M.Bohner jakou sou\u010D\u00E1st definice fok\u00E1ln\u00EDch bod\u016F. Kdy\u017E je tato podm\u00EDnka na j\u00E1dro spln\u011Bna pouze do jist\u00E9ho kritick\u00E9ho indexu m , pak musej\u00ED b\u00FDt tradi\u010Dn\u00ED podm\u00EDnky, jako jsou fok\u00E1ln\u00ED body, konjugovan\u00E9 intervaly, implicitn\u00ED Riccatiho rovnice a \u010D\u00E1ste\u010Dn\u00E9 kvadratick\u00E9 funkcion\u00E1ly, nahrazeny novou podm\u00EDnkou. Tato nov\u00E1 podm\u00EDnka je odvozena jako nez\u00E1pornost (pozitivn\u00ED semidefinitnost) blokov\u011B-tridiagon\u00E1ln\u00ED matice reprezentuj\u00EDc\u00ED zbytek funkcion\u00E1lu I za indexem m na vhodn\u00E9m podprostoru. Aplikace tohoto v\u00FDsledku zahrnuj\u00ED diskr\u00E9tn\u00ED Jacobiovu podm\u00EDnku, sjednocen\u00ED nez\u00E1pornosti a pozitivity I do jedin\u00E9ho tvrzen\u00ED a vylep\u0161en\u00FD v\u00FDsledek pro speci\u00E1ln\u00ED p\u0159\u00EDpad - diskr\u00E9tn\u00ED varia\u010Dn\u00ED po\u010Det. Uveden\u00FD v\u00FDsledek je nov\u00FD, i kd"@cs . . . . . "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. Applications of our result include the discrete Jacobi condition, a unification of the nonnegativity and positivity of I into one statement, and an improved result for the special case of the discrete calcul" . "1" . . "000220541300005" . "266" . "RIV/00216224:14310/04:00011373" . "Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control" . "P(GA201/01/0079)" . . . "Ekvivalentn\u00ED podm\u00EDnky s nez\u00E1pornost\u00ED kvadratick\u00E9ho funkcion\u00E1lu v diskr\u00E9tn\u00EDm optim\u00E1ln\u00EDm \u0159\u00EDzen\u00ED"@cs . "[59DED9332F5E]" . "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. Applications of our result include the discrete Jacobi condition, a unification of the nonnegativity and positivity of I into one statement, and an improved result for the special case of the discrete calcul"@en . "1"^^ . . "Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control" . "Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control"@en . "0025-584X" . . "Ekvivalentn\u00ED podm\u00EDnky s nez\u00E1pornost\u00ED kvadratick\u00E9ho funkcion\u00E1lu v diskr\u00E9tn\u00EDm optim\u00E1ln\u00EDm \u0159\u00EDzen\u00ED"@cs . . "563078" . "Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control"@en . "12"^^ . "2"^^ . . "Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Conjugate interval; Conjoined basis; Riccati difference equation; Discrete Jacobi condition"@en . . "Zeidan, Vera" . . . "Mathematische Nachrichten" . "14310" .