2
votes
2answers
99 views

sensitivity analysis in conic optimization

I have a conic optimization of the form: $\min_x \langle c, x \rangle$, s.t. $Ax = b$, $x \in K$. Where $x \in \mathbb{R}^{n}$, $A$ is an $m \times n$ matrix, $b \in \mathbb{R}^m$, $K$ is a self ...
1
vote
1answer
66 views

optimization of inverse matrix with constraint on matrix elements

everyone! I have this optimization problem with constraint. D and T are symmetric matrice, where T is known and D is the unknown parameter. x and v are two known p-dimensional vectors. The objective ...
22
votes
2answers
806 views

An Interesting Optimization Problem

You are given n non-negative integers $a_1, a_2 ,, a_n$. In a single operation, you take any two integers out of these integers and replace them with a new integer having value equal to difference ...
4
votes
2answers
132 views

Minimax theorem on a non convex domain

A minimax theorem is a theorem which states that under certain conditions on $\mathcal{X}$, $\mathcal{Y}$ and $f$: $$ \inf_{x \in \mathcal{X}}{\sup_{y \in \mathcal{Y}}{f(x,y)}} = \sup_{y \in ...
3
votes
1answer
142 views

Equivalent method for maximum likelihood estimation of covariance parameters

My goal is to estimate the parameters of a covariance matrix $\Omega$, by maximizing the following log-likelihood function: $$\log L(\vec\tau, \rho, \sigma \mid W, X) = -m\ln(\left | \Omega \right |) ...
2
votes
2answers
115 views

Survey on Compared Running Time: Ellipsoid Method vs. Simplex Method

If you look through papers on the Ellipsoid Method, there is a large agreement, that the Ellipsoid Method, although theoretically polynomial, is in practice way slower than the Simplex Method. ...
1
vote
0answers
78 views

Interior point optimisation using big M for L1 norm on linear system using Dikin's Affine method

I am a 4th year undergrad surveying student studying computations, specifically $L_{1}$ norm minimisation of residuals in large data sets. To start with (and probably to finish with) I'm using a set ...
0
votes
1answer
279 views

Nonconvex optimization problem

I have a nonconvex optimization problem. It is actually optimizing a linear objective function over a set of linear constraints and a set of nonlinear, non convex constraints. Is this problem ...
0
votes
2answers
113 views

Rewrite optimization objective

Hi, I wanted to ask, under which conditions can one rewrite the optimization objective $\min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s$ as $\min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t$ I have particular ...
0
votes
0answers
62 views

Big eigenvalues of a special stochastic matrix

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 ...
2
votes
1answer
307 views

Maximizing supermodular functions

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 information about a ...
1
vote
1answer
672 views

Schur complement and negative definite matrices

Hello, My question regards to the Schur complement lemma. Consider the matrix $M=\left( \begin{array}{cc} A & B\\\ B^T & C \end{array}\right) $. According to the lemma $M\geq0$ iff $C>0$ ...
0
votes
1answer
454 views

Finding linearly independent columns of a large sparse rectangular matrix

I have a problem that necessitates solving a large non-negative least-squares problem. My matrix A is large, sparse, highly rectangular (num rows >> num cols) and nearly binary. However, A is not ...