Tagged Questions
0
votes
0answers
33 views
Minimization/maximization of Sum-Product cost functions
I am a little rusty in optimization. Typically in digital detection/decoding one encounters a sum-product cost function. Mathematically, this may represented by
\begin{align}
J(X)=\sum_i\prod_j ...
4
votes
2answers
128 views
Finding good approximation for $x^{1/2.4}$
I would like to a good (8 bits accuracy) approximation for $x^{1/2.4}$ in the range $[0, 1]$. This transform is used for converting linear intensities to SRGB compressed values, so it's important that ...
1
vote
0answers
61 views
Optimization over function spaces
There are many methods to solve optimization over standard spaces such as real and complex numbers or vector spaces of these. In my case I have a vector space of functions of a real value to find.
...
1
vote
1answer
191 views
how to compute the gradient of a function at an extremal point
I am writing a computer program that searches for the minimum of a multivariate function $f: \mathbb{R}^n \to \mathbb{R}$.
This function is in fact the sum of many functions:
$$f(x) = \sum_{i=1}^m ...
1
vote
3answers
247 views
Constrained optimization: equality constraint
I have this very general problem (for $n>2$):
$$
\begin{align}
& \max Z = f(x_1,\ldots ,x_n) \\[10pt]
\text{s.t. } & \sum_{i=1}^{n} x_i = B \\[10pt]
& x_i \geq 0
\end{align}
$$
Assume ...
0
votes
0answers
111 views
Can this non-linear optimisation problem be converted to a linear?
I have to minimize the function: $F(x)$
$F(x) = \sum_{i=1}^{M}||x_{i+1} - x_i - K(\frac{x_{i+1} + x_i}{2})||^2 + ||x_1-c_1||^2 + ||x_N-c_2||^2$ , where $x$ is a vector of $N$ scalars, $c$ are ...
0
votes
0answers
82 views
How to optimize nonlinear goal under linear constraints?
I have a "linear" equation set as follows, with nonlinear optimization goal.
P(0) + P(1) = 1
P(0, 0) + P(0,1) = P(0)
P(0) < 1
P(1) < 1
P(0,0) > 0
P(0,1) > 0
...
9
votes
2answers
384 views
A numerical optimization problem with a convolution in the constraint
I have a problem of the following form:
minimize $\|Dx\|_2$
subject to $\|x*x\|_2 = 1$
where $x\in\mathbb R^n$, $D$ is a given diagonal matrix of positive entries, and $*$ represents convolution, ...
