Hi all -- what would be good methods (and/or software packages) to try for solving a problem minimizing a quadratic function $f(x) = \sum_{i=1}^N{(x_i - y_i)^2}$, where some constr …

Caveat up-front: I'm not a mathematician, so please excuse any stupidity/ignorance that follows. First, let me explain what I'm trying to do: I want to choose a function that maxim …

Motivation: The following problem arose in [1] while studying the vertical distribution of the zeros of the Riemann zeta-function. At the time, my collaborators and I were unable t …

Hello everyone, I have a problem and I really don't know what kind of mathematical method should I apply to solve or model my problem. I would be thankful If anyone can give me so …

Made a crucial mistake in the problem formulation; please delete.

Suppose we have a graph on $n$ nodes. We would like to assign to each node either a $+1$ or a $-1$. Call this a configuration $\sigma \in \{+1,-1\}^n$. The number of $+1$s that we …

Let $(N,A,s,t,u)$ be a network with node set $N$, arc set $A$, source $s\in N$, sink $t\in N$ and capacity vector $u\in\{1,2,\ldots,T\}^A$, and let $x=(x_a)_{a\in A}$ be a maximum …

I'm having troubles with searching for analytical solution of following problem. Let we work in 3-D space and have the set of points (uniform net at cube's facets): $(−1,−1+j∗h,−1 …

The title says it all :) Given a submodular function (take the rank function of a matroid, for a concrete example) $f:\{0,1\}^n\rightarrow \mathbb{R}$, we can extend it to a conve …

Suppose $\phi({\bf x},{\bf z})$ is a continuous function of two arguments, $\phi: {\mathbb R}^N \times Z \rightarrow {\mathbb R}$, where $Z \subset {\mathbb R}^m$ is a (non-emp …

I want to solve the follong QCQP problem: $$ \mbox{Minimize}\quad\beta^TA\beta+\mu\Omega(\beta)$$ $$ \mbox{s.t.}\quad\beta^TB\beta=1 \quad\mbox{and}\quad\beta\ge0 $$ where $A$ an …

I am trying to find a book or a paper, which explains, how and why the Sherali-Adams relaxation method works. The original paper (1990) is difficult for me to understand. I need a …

Let $a_1,a_2,..,a_n\in\mathbb{R}^m$, $n>m$ and the points are in general position meaning, no hyperplane contains more than $m$ points. Define a polyhedron $$P=\{x\in\mathbb{R}^m …

Hello, everyone! Suppose that there are two Hermitian matrices $A,B$ and a unit vector $\mathbf{x}$, then how to calculate the relative entropy of the quadratic forms determined b …

I am familiar with the conjugate function of the vector norm, which uses the concept of dual norm and is defined as follows: $\|\mathbf{y}\|_p^*=\max_{\mathbf{x}}\left(\mathbf{x}^ …