16 votes

Optimal search puzzle

You can solve the problem via dynamic programming. For $n\in\{1,\dots,t\}$, let $V(n)$ be the minimum expected number of steps starting from $n$. Then $V(1)=0$ and otherwise $$V(n) = 1+\min\left(\...
RobPratt's user avatar
  • 4,959
15 votes

Optimal search puzzle

Because using the random operator destroys any potential gain from a previous subtraction, the optimal strategy must look like the one stated in the question. The solution of @RobPratt showed that ...
Karl Fabian's user avatar
  • 1,159
4 votes

optimization over moving domains

$\newcommand\R{\mathbb R}$The answer is no. E.g., let $A=B=\R$, $B_a=[1-a^2,2]$ for $a\in A$, and $\ell(b)=b^3-3b$ for $b\in B$. Then $\ell(b)$ and $B_a$ are perfectly smooth, but $L$ is not ...
Iosif Pinelis's user avatar
1 vote

nonlinear equation problem

Here is an existence argument on the lines of the proof of the Perron-Frobenius theorem via the Brouwer fixed point theorem. Note that from the equation, since by assumption $a_i>0$ and $K_{ji}\ge0$...
Pietro Majer's user avatar
  • 54.5k

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