Physics+ MIN/MAX of Functional: UNIZOR.COM - Physics+ 4 All - Variations
Автор: Zor Shekhtman on UNIZOR Education
Загружено: 2025-07-10
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UNIZOR.COM - Creative Mind through Art of Mathematics
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Lagrangian - Definition of Min/Max of Functional
In this lecture we will discuss a concept of a local minimum or maximum of a functional.
Function f0(x) is a local minimum of functional F() if for any direction defined by function h(x) there exist a real positive number τ such that
F(f0(x)) ≤ F(f0(x)+t·h(x))
for all 0 ≤ t ≤ τ
Analogously,
Function f0(x) is a local maximum of functional F() if for any direction defined by function h(x) there exist a real positive number τ such that
F(f0(x)) ≥ F(f0(x)+t·h(x))
for all 0 ≤ t ≤ τ
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