Weber: One of the first books in economics to deal with the calculus of variations
Finally, in the last section, we apply the Duality Principle to the calculus of variations
on time scales.
The problem of the calculus of variations
on time scales under consideration has the form
This edition has been expanded to include chapters on: integral equations, calculus of variations
, tensor analysis, time series, and partial fractions.
According to her Web site, her research focuses on calculus of variations
and symmetry methods for differential equations.
Schwartz, Dynamic Optimization: The Calculus of Variations
and Optimal Control in Economics and Management.
Such microstructure largely determines the macroscopic properties of the material, but the prediction of its morphology remains poorly understood, and is related to deep unsolved problems in the calculus of variations
He includes the calculus of variations
and optimal control, historical notes on the calculus of variations
, preliminaries on the simplest problems, necessary conditions for local minima, sufficient conditions for the simplest problems, extensions and generalizations, applications, optimal control problems, simplest problems in optimal control, extension of the maximum principal, and linear control systems.
In the discrete calculus of variations
and control problems it is assumed that [R.
The theoretical section begins with a self-contained chapter on parameter optimization, presented via 14 theorems, then covers the calculus of variations
, the minimum principle of Pontryagin and Hestenes, and the Jacobi test.
multiplication loops of locally compact topological translation planes; Lie groups which are the groups topologically generated by all left and right translations of topological loops; the inverse problem of the calculus of variations
for second order ordinary differential equations: existence of variational multipliers, in particular, of multipliers satisfying the Finsler homogeneity conditions, and Riemannian and Finsler metrizability; metric structures associated with Lagrangians and Finsler functions variational structures in Finsler geometry and applications in physics (general relativity, Feynmam integral); Hamiltonian structures for homogeneous Lagrangians.
He has organized the main body of his text in nine chapters devoted to the calculus of variations
, Lagrangian mechanics, motion in a central-force field, collisions and scattering theory, and a wide variety of other related subjects.
Applications to regular and bang-bang control; second-order necessary and sufficient optimality conditions in calculus of variations
and optimal control.
Chapters cover the following standard topics: the calculus of variations
, Lagrangian mechanics, Hamiltonian mechanics, motion in a central field, collisions and scattering theory, motion in a non-inertial frame, rigid body motion, normal-mode analysis, and continuous Lagrangian systems.
3) arise as second variations in nonlinear calculus of variations
and optimal control problems, see e.