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# Questions tagged [oc.optimization-and-control]

Operations research, linear programming, control theory, systems theory, optimal control, game theory

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### Leech lattice shortest vector vs other 23 cases and E8 cases

In this paper by Viazovska, she said that: "The E8-lattice sphere packing 𝒫E8 is the union of open Euclidean balls with centers at the lattice points and radius $1/\sqrt{2}$." So I think ...
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### Curve fitting with "rough" loss functions

Many real-valued classification and regression problems can be framed as minimization in the following way. Setup: Let $\Theta \in \mathbb{R}^p$ be the parameter space that we are searching over. For ...
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### Relation between the left-dominant eigenvectors (eigenvector corresponding to 0 eigenvalue) of two Laplacian matrices

Let $G_1=(v,\epsilon_1)$,$G_2=(v,\epsilon_2)$ be two graphs with the same set of vertices and $\epsilon_1 \subset \epsilon_2$. $L_1$ and $L_2$ be the Laplacian matrices associated with graph $G_1$ and ...
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### How much "room" in inequality $\displaystyle \int_a^b \varphi' ov ~\mathrm{d}x \leq 0$

Let $[a, b]$ be a nonempty interval, $o \in C^1([a, b])$ be such that $o>0$ and $o'<0$ and assume we found some $v \in L^\infty(\mathbb{R})$ such that \begin{equation}\tag{1}\label{1} \int_a^b \...
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### Can a real quartic polynomial in two variables have more than 4 isolated local minima?

This question: "Can a real quartic polynomial in two variables have at most 4 isolated local minima?" came up in this post on Math SE but with no answer so far. Finding examples of 4 ...
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1 vote
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### Is non-convex optimisation really in NP class?

Crossposted on Mathematics SE I've seen in many optimisation papers the statement that general non-convex optimisation problem is NP-hard. If we assume that non-convex optimisation is in NP class, it ...
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### A simple stochastic game

An individual, henceforth called the runner starts at the center of an open two dimensional square $\Omega$ of side length $r \geq 2$. At each turn, a vector $x \in S^1$ is chosen uniformly at random, ...
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### Matrix optimization to find ideal embedding

Basically, I am trying to find the embeddings so I can approximate $K \approx M(\vec{\phi})$. The embeddings are for each one of my samples $\vec{\phi}(x_i) \in \mathbb{R}^D$ so I thought it should ...
### Given a set of vectors how to pick $M$ such that sum of maximums of coordinates is maximized?
I asked the same on math.Stackexchange. I have $n$ (say $n = 300$) vectors $v_1,\dots,v_n$. Each of them has $K$ coordinates (say $K = 30$). For vector $v_j$ I denote it's coordinates as \$v_{j1},\...