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Results tagged with oc.optimization-and-control
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user 15626
Operations research, linear programming, control theory, systems theory, optimal control, game theory
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Has anybody ever seen something like this (optimization problem / variational calculus)
Hi all,
I'm trying to minimize the following integral : $ \int_{0}^{\pi/2} \frac{\int_{0}^{x} \sqrt{r(\theta)^2 + r'(\theta)^2}d\theta}{\sin(x)} dx $ with boundary values r(0)=1 and r(pi/2)=0. As yo …
- 81
2
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1
answer
187
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Conditions ensuring extrema are twice continuously differentiable?
For a functional $J[y]=\int_{a}^{b}F(t,y,y')dt$, are there any conditions that ensure extrema over the class of piecewise continuously differentiable functions are all in $C^2[a,b]$?
- 81
2
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1
answer
416
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Proving a variational problem has no solutions
Consider the following integral
$ \int_{0}^{\frac{\pi}{2}} \left( \sqrt{y(x)^2 + y'(x)^2} \left( \ln \left( \frac{\sin(x)}{1 -\cos(x)} \right) + \frac{\pi}{2} \right) + \frac{\pi}{2} y'(x) + 1 \right …
- 81