# optimization's questions - Chinese 1answer

11.786 optimization questions.

### How to find optimum (least square error) “square splitting circular arc” with given two centroids? [on hold]

0 answers, 24 views geometry optimization circle centroid
I am looking for an analytic solution for the following problem. A unit square is given. Coordinates of two points inside the square are given. What is the best circular arc which splits the square in ...

### Binomial inequality

I have two binomial expressions. \begin{align} mm_{1}\binom{N(d+1)+n}{n}\tag{1}\\ \binom{N+n+1}{n+1}\tag{2} \end{align} wher $n,m,m_1,d$ are constants and only $N$ varies. Now we have the ...

### 1 Optimization problem where the support of a random variable depends on the value of a decision variable

Suppose we have a dynamic program / Markov decision process where in the objective we have something like this: $v_t(s)=\max\limits_{u_1,u_2} \{r_t(s,u_1,u_2) + E[v_{t+1}(u_1+\min(u_2,\epsilon))]\}$, ...

### 2 Need to create $3-4$ different box sizes and to minimize material waste for a set of $n$ objects that need to fit into these boxes

2 answers, 61 views optimization operations-research
Excuse the non-mathematical way I've phrased the question. I have the following problem: I have $N$ square paper documents with side lengths between $150$mm and $860$mm. I know each document side's ...