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(\...

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 ...

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 ...

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 $K_{ji}\ge0$...

Only top scored, non community-wiki answers of a minimum length are eligible

#### Related Tags

oc.optimization-and-control × 1113convex-optimization × 201

nonlinear-optimization × 171

linear-algebra × 144

matrices × 103

linear-programming × 87

pr.probability × 79

global-optimization × 68

reference-request × 66

fa.functional-analysis × 64

mg.metric-geometry × 61

na.numerical-analysis × 60

combinatorial-optimization × 53

co.combinatorics × 52

algorithms × 43

dg.differential-geometry × 42

graph-theory × 39

calculus-of-variations × 39

stochastic-processes × 36

real-analysis × 34

convexity × 33

computational-complexity × 32

ds.dynamical-systems × 31

inequalities × 31

ca.classical-analysis-and-odes × 30