Calculus of variations and optimal control; optimization Second variation and sufficient conditions Concept
Field of extremals
Summary
A field of extremals is a family of solutions of the Euler–Lagrange equation that covers a region of the plane. Exactly one curve of the family passes through each point of the region. The slopes of the curves define a slope function on the region. Embedding an extremal in such a field is the key step of the Weierstrass theory of sufficient conditions for a strong minimum. It is the classical counterpart of the method of characteristics for the Hamilton–Jacobi equation.
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| Tag | K4DFT3H9BJ |
|---|---|
| URI | m2://K4DFT3H9BJ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 49K05 |
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