All Questions
4
questions
1
vote
0
answers
127
views
Minimizing the magnitude of the sum of a vector of complex numbers with an integer constraint
Let $h_{1}, ..., h_{N} \in \mathbb{C} $
Consider minimizing the function below:
$ \min \left| \sum\limits_{i=1}^N h_{i} x_{i} \right| $
with the constraints $x_{i}^2 = 1$
i.e., $x_{i}$ can only take ...
- 11
3
votes
1
answer
79
views
Sum of integers closest to a given number
I have the following problem at hand:
Given an odd number $n > 7$, find a set of non-negative integers $m_7$, $m_8$, ..., $m_{13}$ and $m_{14}$, such that the sum
$m_7\cdot 7 + m_8\cdot 8 + ... + ...
- 41
3
votes
0
answers
53
views
How to find smallest sum of denominators so that sum of fractions is less than or equal to 1, given the numerators? [closed]
Given $n$ positive integer numbers $a_1, a_2, \dots, a_n$, how do I find $n$ positive integer numbers $b_1, b_2, \dots, b_n$, so that
$$\frac{a_1}{b_1} + \frac{a_2}{b_2} + \dots + \frac{a_n}{b_n} \leq ...
- 131
1
vote
1
answer
30
views
Searching for the right partitions
I have a set of integers $U$ with cardinality $311$ and whose sum is 500 dollars.
I want to group all the elements of this set into three different subsets:
The sum of the elements of subset $A$ is $...
