Given a matrix $M$ of size $n\times n,$ we write its different eigenvalues by $x_1,x_2,\ldots,x_m$ with $m\leq n$ such that $|x_1|>|x_2|>|x_3|>\cdots|x_m|,$ and call $x_2\doteq |\l …

In usual formulation of conjugate gradient algorithm initial search direction is taken to be the residual (so residual and search direction spans Krylov subspace). However, in case …

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 …

I am going to post a particular example for the sake of clarity. One needs to maximize a real function $F = a_1a_2 + a_2a_3 + \cdots + a_{n - 1}a_n + a_na_1;$ wit …

Let me explain what I mean: The width of the average person varies, perhaps with a normal distribution. Given a specific variance, how many people (on average) can sit side-by-si …

I have a real supermodular objective function which I want to maximize with constraint. The constraint is on the size, like |A|=k . I am wondering if anyone can give me more inf …

Denote $U=\{(x_1,x_2,...,x_n):x_j\in(0,1) (1\le j\le n),\sum_{j=1}^nx_j=1\}$. Let $f_i=f_i(x_1,x_2,...,x_n)$ ($1\leq i\leq n-1$) be $n-1$ real functions which satisfy: $\prod_{i …

I have the following semi-infinite programming problem: I need to minimize a strictly convex real-valued function $f:\mathbb R^n\to\mathbb R$ subject to infinite linear constraints …

Consider the following optimization problem. Let $n, m \in \mathbb N$ and $0 < p_1 \leq \ldots \leq p_n ~ (p_i \in \mathbb R)$ be constant. The feasible region is described by a …

I have a function $f:\mathbb{R}^{50} \rightarrow \mathbb{R}$ and I need to compute the Lipschitz constant of $f$ to solve an optimization problem using a specific algorithm. Does a …

I come across a problem like $\max {\frac{1+v}{1-u}}$ $s.t.~$ $ux^2+vy^2-xy\ge0$ $\forall x,y\in\mathbb{R}$ I do not know much of optimization. What I have done is that $ux^2+vy …

Define a functional space of functions of the form $F(t)=p_1 exp^{-\mu_1(\delta-t)}+p'_1 (1-exp^{-\mu_1(\delta-t)}))$. $p_1,p'_1,\delta,\mu$ are parameters in [0,1] and trivially, …

The Farkas Lemma says that if a system of linear inequalities implies yet another linear inequality, then this last inequality can be obtained by taking a positive linear combinati …

I want to solve a matrix $\Omega$ from a equation $\sum_k (\Omega + \Theta_k)^{-1} = Q$. The $Q$ and $\Theta, \forall k=1...K$ are known, and are positive definite matrices. $\Omeg …

I am interested in solving the following equality constrained quadratic (?) problem. \begin{align} \min_{u^{H}u=1}~(u^{H}A_1u) \\ s.t.~ u^{H}A_2u=0 \end{align} $A_1$ and $A_2$ …