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

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 come to a point in my PhD research were i need to prove that a particular decision procedure is decidable or not. And if i can solve the sub-problem described below, i shall …

Consider the following optimization problem: Maximize $||X||$, subject to $X$ being Hermitian (or symmetric, if you prefer) and a bunch of semidefinite constraints on $X$. I want t …

i am trying to solve a general linear objective function with non-linear constraints. Can someone help me solve this. Here is an example of one problem i am trying to solve, min …

Consider $J = \sum_{i=0}^{N}y_{i-1}x_{i}y_{i+1}$ where $+$ and $-$ in the indices are mod $N+1$. Let $x_{i} = 1 - y_{i} \in {0,1}$. What are some of the tools useful and relaxation …

The optimization problem is: maximize $$\min(\sum\limits_{i=1}^N \log\left(a_{1,i}+\frac{b_{1,i}}{c_{1,i}+d_{1,i}x_i}\right),\sum\limits_{i=1}^N \log\left(a_{2,i}+\frac{b_{2,i}}{c …

I posted an earlier version of this question on math.stackexchange almost a week ago but have not had any replies. I'm recasting the problem in light of new understanding. I'd like …

Is there any known (symbolic) method that solves a system of equations/inequalities that have trigonometric functions on the left-hand side of the system? Ex) Find $x,y,\theta \i …

Is there an algorithm to check if a given (possibly nonlinear) function f is always positive? The idea that I currently have is to find the roots of the function (using newton-rap …

Dear all, I've got a SDP problem as follows: $\min_{{\bf H}\succeq0}\quad trace({\bf H}) - {\bf a}^{\top}{\bf H}{\bf b}$, where ${\bf a}$ and ${\bf b}$ are two constant vectors. …

% Lyapunov exponent of Lorenz equation clc clear all % ---------- Lyapunov Exponents ---------- % n = 3; % number of state variables consist of : theta1, d/(dt)*theta1 …

I have a set of five equations which can be described as follows: $m_{i}=\frac{k_{1}}{(x+a)^{i}} + \frac{k_{2}}{(b+d)^{i}}+ \frac{k_{3}}{c^{i}}$ for i=1 to 5 where $$\eqalign{ k …

lets say we have the following optimization problem: min max $|Ax|$ . s.t. $Hx \leq h$ . and $x \in {-1,1}$ This is minimax problem that can be cast into an Integer Linear Pr …

Let $C$ be size $n \times n^{2}$. Let $B$ be size $2^{g(n)} \times n^{2}$ where $g(n) > n$. There is only one $\mathcal{1}$ per row of $C$ and remaining entries of $C$ are $\mathc …