Coupled intervals in the discrete calculus of variations: necessity and sufficiency

DOI10.1016/S0022-247X(02)00495-XzbMath1032.49038OpenAlexW1988500649MaRDI QIDQ1856987

Roman Šimon Hilscher, Vera Zeidan

Publication date: 11 February 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00495-x

zbMATH Keywords

positivitynonnegativitycoupled intervaldiscrete calculus of variationsdiscrete quadratic functionalvariable endpointsconjugate interval

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Linear-quadratic optimal control problems (49N10) Discrete version of topics in analysis (39A12) Difference equations, scaling ((q)-differences) (39A13) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (7)

Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals ⋮ Coupled intervals for discrete \(p\)-degree functional ⋮ Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey ⋮ Symmetric three-term recurrence equations and their symplectic structure ⋮ Optimality conditions for discrete calculus of variations problems ⋮ Time scale embedding theorem and coercivity of quadratic functionals ⋮ Coupled Intervals in the Discrete Optimal Control

Cites Work

• Disconjugacy for linear Hamiltonian difference systems
• Qualitative properties of Hamiltonian difference systems
• Jacobi condition for elliptic forms in Hilbert spaces
• A discrete interpretation of Reid's roundabout theorem for generalized differential systems
• Quadratic functionals with general bounday conditions
• Disconjugacy and transformations for symplectic systems
• Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices
• Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• Discrete optimal control: The accessory problem and necessary optimality conditions
• Sufficient conditions for variational problems with variable endpoints: Coupled points
• An approach to nonlinear programming
• Second Order Sufficiency Criteria for a Discrete Optimal Control Problem
• Coupled Points in the Calculus of Variations and Applications to Periodic Problems
• Sufficiency Criteria via Focal Points and via Coupled Points
• Positivity of Block Tridiagonal Matrices
• Constrained Regular LQ-Control Problems
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