Hi, I have a cost function of the form F(X) = tr{X'AX}+tr{X'B} , s.t. X'X=I X is a m by n, m>n matrix with orthonormal columns. A is symmetric m by m, not necessary positive defi …

I was wondering, whether you could point me to some tools with which I could tackle the following "infinite-dimensional linear programming" problem: Notation: $a=1,2,\ldots, A$, …

A delta-convex (d.c.) function is one which can be written as the difference of two convex functions. The space of d.c. functions includes all C2 functions, and is interesting bec …

I want to prove that the following two models are equivalence. Is there any suggestion that how could be proved? First model: $$\min ~~ E | y| $$ $$~~~~~~~~~~~~s.t. ~~\langle I, …

$\min_{\beta}\beta^{T} A \beta$ $s.t. \ \beta^{T} C \beta=1\ and\ \beta\geqslant 0$ Here $A,C\in \mathbb{R}^{M\times M}$, $\beta \in \mathbb{R}^{M}$ I saw in one paper saying t …

I am trying to read this paper and have gotten stuck. The author considers the problem of minimizing a convex function whose gradient has Lipschitz constant $M$ and considers the s …

Given a connected graph $G=(V,E)$ with a weight function $w:E\to\mathbb{R}$ and a subset $E_0\subseteq E$ such that the subgraph $(V,E_0)$ is connected, I am looking for a sequence …

The Motzkin-Straus theorem says that the global optimum of the quadratic program $$\max f(x)=\frac{1}{2} x^{t}Ax,\qquad \mbox{ subject to }\sum x_{i}=1 \mbox{ and } x_{i}\geq 0,$$ …

Hi, I have a matrix of the form $A=VDV^H$, where $V$ is a $M \times 2M$ complex matrix, $D$ is a $2M \times 2M$ diagonal real matrix, thus the dimension of $A$ is $M \times M$. …

Hi I have the following problem whose solution has lured me for some months now.... All matrices are complex $N\times N$. Let $A$ be a positive definite matrix with all eigenvalue …

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is: Lemma (Gibbs). $f_1,f_ …

Consider the linear wave equation : $$z_{tt}=\Delta z + k(x) z + h(t) , \; in \; \Omega\times (0,T)$$ Are there sufficient conditions on the functions $k(x)$ and $h(t)$ for which …

Disclaimer: I posted the same question on math.stackexchange. However, the FAQ suggests to post research-level questions in this forum. Question: Given a function $q: \mathbb R^{N …

Hi I have the following problem (and a conjecture which holds in Matlab). Given an $N\times N$ matrix $H$, represent it by its $2N\times 2N$ real-valued representation (which I wi …

I need to consider the vehicle routing problem(VRP) with following constraints: 1) The number of vehicle is $N$. 2) The number of deport is $M$. 3) Different vehicles have diffe …