. . . . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "P(GA201/01/0079)" . "Sdru\u017Een\u00E9 intervaly v diskr\u00E9tn\u00EDm optim\u00E1ln\u00EDm \u0159\u00EDzen\u00ED"@cs . . "1"^^ . . . "RIV/00216224:14310/04:00011340!RIV09-GA0-14310___" . . "558930" . "2"^^ . . "10" . "\u0160imon Hilscher, Roman" . . "Sdru\u017Een\u00E9 intervaly v diskr\u00E9tn\u00EDm optim\u00E1ln\u00EDm \u0159\u00EDzen\u00ED"@cs . . "000186751100004" . "14310" . . . "In this paper, we investigate the nonnegativity and positivity of a quadratic functional I with variable (i.e., separable and jointly varying) endpoints in the discrete optimal control setting. We introduce a coupled interval notion, which generalizes (i) the conjugate interval notion known for the fixed right endpoint case, and (ii) the coupled interval notion known in the discrete calculus of variations . We prove necessary and sufficient conditions for the nonnegativity and positivity of I in terms of the nonexistence of such coupled intervals. Furthermore, we characterize the nonnegativity of I in terms of the (previously known notions of) conjugate intervals, a conjoined basis of the associated linear Hamiltonian system, and the solvability of an implicit Riccati equation. This completes the results for the nonnegativity that are parallel to the known ones on the positivity of I . Finally, we define partial quadratic functionals associa" . . . "1023-6198" . . "V tomto \u010Dl\u00E1nku studujeme nez\u00E1pornost a pozitivitu kvadratick\u00E9ho funkcion\u00E1lu I s prom\u011Bnn\u00FDmi (tj. separovan\u00FDmi \u010Di obecn\u00FDmi) konci v probl\u00E9mu diskr\u00E9tn\u00EDho optim\u00E1ln\u00EDho \u0159\u00EDzen\u00ED . Zav\u00E1d\u00EDme pojem sdru\u017Een\u00E9ho intervalu , kter\u00FD zobec\u0148uje (i) pojem konjugovan\u00E9ho intervalu, kter\u00FD je zn\u00E1m pro probl\u00E9my s pevn\u00FDm prav\u00FDm koncem, (ii) pojem sdru\u017Een\u00E9ho intervalu, kter\u00FD je zn\u00E1m v diskr\u00E9tn\u00EDm varia\u010Dn\u00EDm po\u010Dtu . Dokazujeme nutn\u00E9 a posta\u010Duj\u00EDc\u00ED podm\u00EDnky pro nez\u00E1pornost a pozitivitu I pomoc\u00ED neexistence takov\u00FDch sdru\u017Een\u00FDch interval\u016F. Nav\u00EDc, charakterizujeme nez\u00E1pornost I pomoc\u00ED (ji\u017E d\u0159\u00EDve zn\u00E1m\u00FDch pojm\u016F) konjugovan\u00FDch interval\u016F, izotropick\u00FDch b\u00E1z\u00ED p\u0159\u00EDslu\u0161n\u00E9ho line\u00E1rn\u00EDho Hamiltonovsk\u00E9ho syst\u00E9mu, \u010Di \u0159e\u0161itelnosti implicitn\u00ED Riccatiho rovnice. Tyto v\u00FDsledky dopl\u0148uj\u00ED v\u00FDsledky o nez\u00E1pornosti I , kter\u00E9 jsou paraleln\u00ED k v\u00FDsledk\u016Fm o pozitivit\u011B I . V z\u00E1v\u011Bru \u010Dl\u00E1nku definujeme \u010D\u00E1ste\u010Dn\u00E9 kvadratick\u00E9 funkcion\u00E1ly p\u0159idru\u017Een\u00E9 k I a (silnou) regularitu I a studujeme"@cs . "Coupled intervals in the discrete optimal control"@en . "Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Coupled interval; Conjugate interval; Conjoined basis; Riccati difference equation"@en . "2" . "36"^^ . "Coupled intervals in the discrete optimal control"@en . . "Coupled intervals in the discrete optimal control" . "Journal of Difference Equations and Applications" . . . "RIV/00216224:14310/04:00011340" . "In this paper, we investigate the nonnegativity and positivity of a quadratic functional I with variable (i.e., separable and jointly varying) endpoints in the discrete optimal control setting. We introduce a coupled interval notion, which generalizes (i) the conjugate interval notion known for the fixed right endpoint case, and (ii) the coupled interval notion known in the discrete calculus of variations . We prove necessary and sufficient conditions for the nonnegativity and positivity of I in terms of the nonexistence of such coupled intervals. Furthermore, we characterize the nonnegativity of I in terms of the (previously known notions of) conjugate intervals, a conjoined basis of the associated linear Hamiltonian system, and the solvability of an implicit Riccati equation. This completes the results for the nonnegativity that are parallel to the known ones on the positivity of I . Finally, we define partial quadratic functionals associa"@en . "Coupled intervals in the discrete optimal control" . "[ADE44CE465A7]" . "Zeidan, Vera" . .