16
votes
Accepted
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(\...
- 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 ...
- 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 ...
- 106k
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 $K_{ji}\ge0$...
- 54.5k
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