# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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### What is the Euler Lagrange condition for SDEs?

Does the Euler Lagrange condition... $$\frac{d}{dt}\left( \frac{\partial L}{\partial \dot{x}}\right)-\frac{\partial L}{\partial x}=0$$ ...have a meaningful extension to Stochastic Differential ...
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### Derivation of Von Karman Equations

I'm reading Howell's Applied Solid Mechanics to gain background for a research project. I'm struggling with the following derivation in the text that the authors refer to as a "lengthy exercise." The ...
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### Find the maximum and minimum of the function $f$

Find the maximum and minimum of $f(x, y)=xy-y+x-1$ at the set $x^2+y^2\leq 2$. I have done the following: Since the region $x^2+y^2\leq 2$ is closed, $f$ has a maximum and a minimum, which is ...
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### Proof of convergence for the proximal point algorithm

I'm trying to come up with a super simple proof of convergence on the proximal point algorithm, which uses the iteration scheme $x^{i+1} = \mathbf{prox}_{tf}(x^i)$ where $f$ is a closed, convex (...
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### Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
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### Hessian-Matrix positive definite $\iff$ $a$ local minimum?

It is commonly known that if $f$ is twice differentiable, $\nabla f(a) = 0$ and $H_f(a)$ positive definite, $a$ is a local minimum. So, in short: $H_f(a)$ positive definite $\implies$ $a$ local ...