- #1
saminator910
- 96
- 1
Can anyone tell me straightforward information about a way to maximize a certain functional [itex]I[f]=\displaystyle\int_{X} L(f,x)dx[/itex] such that the integral is bounded, [itex]T≥\displaystyle\int_{X}f(x)h(x)dx[/itex]. I really know a minimal amount about functional analysis and calculus of variations, but I've looked at things like Hamiltonians and I don't know if they apply to this problem. Intuitively I see this as a problem that would be solved with Lagrange multipliers if it we weren't talking about functions and functionals, ie [itex]\vec{f}\cdot \vec{h}=T[/itex] is a linear constraint, [itex]∇I(x_{1},...,x_{n})=\lambda \vec{h}[/itex]. We would then solve systems of equations [itex]\lambda h_{i}=\frac{\partial I}{\partial x_{i}}[/itex]. Any help is greatly appreciated.