Tagged Questions
1
vote
1answer
37 views
On norm selection for the solution of an overdetermined linear system
I am considering the following linear system:
$Ax = b$
Where:
$A$ is $9000 \times 139$
$x$ is $139 \times 1$ and sparse
$b$ is $9000 \times 1$
Most of the resources I have found online point to ...
0
votes
0answers
34 views
Find a number that minimizes distance to a vector of sets of numbers
Assumptions
$V$ is a vector of sets $V_1,V_2,...,V_n$ of numbers:
$V=[V_1, V_2,..., V_n]^T, \forall_{i=1..n}V_i\subset\mathbb{R}$
$c\in\mathbb{R}$ is constant
$d(V,c)$ is an error metric: ...
1
vote
0answers
115 views
Gradient Descent for Primal Kernel SVM with Soft-Margin(Hinge) Loss
Given the primal objective
$$F({\bf a})=L\sum_{i,j}a_{i}a_{j}k(x_i,x_j) + \sum_{i}max(0, 1-y_i \sum_{j}a_jk(x_i,x_j)$$
for the soft margin SVM, where ${\bf a}=(a_1,...,a_N)$, N being the number of ...
1
vote
0answers
77 views
constrained optimization of dot product
Given a real matrix $A$ find a positive vector $x$ of unit length ($x^T x = 1$) for which $x^T A^T A x$ is minimal (closest to $0$).
A has size about $1000 \times 20$ and can be written as $[ A_P | ...
1
vote
1answer
155 views
Find equation of line such that area formed by line & positive coordinate axis is minimal
Find equation of line passing through $(20,12)$ such that the area of the triangle formed by the line and the positive axis is smallest possible.
Also: $\frac{x}{a}+\frac{x}{b}=1$
where $a, b$ are ...
0
votes
1answer
118 views
parametrize hypersphere
I want to find an $n$-vector $\hat{\theta}$ that maximizes a function $f(\theta)$ subject to the $p$-norm constraint $||\theta||_p = c$.
Is there a general parametrization of $p$-norm hyperspheres ...
1
vote
1answer
182 views
Finding $\min_{\mathbf x} (\mathbf y - \mathbf G\mathbf x)^T(\mathbf y - \mathbf G\mathbf x)$
Let $\mathbf G$ be a given $m \times n$ matrix, $\mathbf y$ a given $m \times 1$ column vector and $\mathbf x$ an unknown $n \times 1$ column vector such that $\mathbf x \ge 0$.
1) How do you find ...
