Sufficiency and the Jacobi Condition in the Calculus of Variations

DOI10.4153/CJM-1986-060-5zbMath0661.49010OpenAlexW2313912395MaRDI QIDQ3810434

Vera Zeidan, Frank H. Clarke

Publication date: 1986

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-1986-060-5

zbMATH Keywords

Hamilton-Jacobi inequalitysufficient conditionsLegendre conditionmatrix Riccati differential equationsWeierstrass' excess functionexistence of weak and strong local minima

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimality conditions for problems involving ordinary differential equations (49K15) Hamilton-Jacobi theories (49L99)

Related Items

Global optimality in the calculus of variations ⋮ Sufficient conditions for variational problems with variable endpoints: Coupled points ⋮ Another Jacobi sufficiency criterion for optimal control with smooth constraints ⋮ Statistical mechanics with homogeneous first-degree Lagrangians ⋮ The minimum plane path for movable end-points and the nonsimultaneous variations ⋮ Symmetries and zero modes in sample path large deviations ⋮ Second-order sufficiency criteria and local convexity for equivalent problems in the calculus of variations ⋮ Extended sufficient conditions for strong minimality in the Bolza problem: applications to space trajectory optimization ⋮ Optimality of extremals for linear systems with quadratic costs ⋮ Sufficiency conditions with minimal regularity assumptions ⋮ Local minimality properties of circular motions in \(1/r^\alpha\) potentials and of the figure-eight solution of the 3-body problem ⋮ Dual sufficient optimality conditions for the generalized problem of Bolza. ⋮ A new sufficiency theorem for strong minima in the calculus of variations