Questions tagged [constrained-optimization]
41 questions
14
votes
2 answers
MLE for normal distribution with restrictive parameters
Suppose that $X_1, . . . , X_n$, $n\geq 2$, is a sample from a $N(\mu,\sigma^2)$ distribution. Suppose $\mu$ and $\sigma^2$ are both known to be nonnegative but otherwise unspecified. Now, I want to find the MLE of $\mu$ and $\sigma^2$. I have drawn…
statwoman
- 541
- 1
- 9
4
votes
2 answers
In optimization, is there a distinction between "implicit/natural" and "explicit/designed" constraints?
For example, I wish to optimization a function which has a log term $\log(x)$
Now the very presence of the log term induces a constraint which says $x > 0$. The case $x = 0 $ might be a bit ambiguous but certainly $x \not< 0$
Now, this to me is some…
Norman
- 297
- 2
- 11
4
votes
2 answers
MSE of correlations
These might be dumb questions but I am having trouble to wrap my head around of a particular problem. I have a sparse count matrix $G $ that I want to optimize which is $N \times p$. Also, I have correlation matrix $C_{ij}$ which is $N \times N$…
eonurk
- 93
- 5
3
votes
2 answers
L1 Regularization vs Constraint
It is my understanding that the these:
\begin{equation}
min_{x}f(x)+\lambda\vert\vert x\vert\vert _{L_{1}}
\end{equation}
\begin{equation}
min_{x}f(x) \text{,}\hspace{5pt}\vert\vert x\vert\vert _{L_{1}}\leq M
\end{equation}
problem formulations are…
user291435
2
votes
1 answer
KKT Conditions for thresholds?
My main question is that when I use Lagrange Multipliers/KKT conditions to perform optimization with threshold constraints, I seem to get contradictory FOC.
Here is a characteristic example:
take an optimization problem like the…
naveace
- 23
- 3
2
votes
0 answers
Can I use xboost as objective function in an optimization problem?
I am working on a marketing optimization problem, where the goal is maximize profit by optimally allocating spend to different products. Constraint is getting at least 1 Million revenue.
As a first step, I built a model to predict the revenue using…
tjt
- 687
- 4
- 13
2
votes
0 answers
Gradient descent finds local minima for a problem that can be formulated as a convex problem
I am trying to find
$$ \min_W \|Y-XW \|_F^2$$ $$s.t. \exists ij, W_{ij}\geq0 $$
where X is input data and Y is the output data we try to fit to. This is a convex optimization problem that can be solved with quadratic programming.
As an exercise, I…
CWC
- 251
- 1
- 5
2
votes
1 answer
Is it possible to optimize correlation coefficient under linear constraint?
I am new to optimization and recently bump into a problem where I have to optimize the correlation coefficient of a series of values with the absolute value of another vector under the linear constraint, but I am not sure if optimization correlation…
flashing sweep
- 433
- 2
- 9
2
votes
1 answer
Resulting shapes when partitioning the constraint matrix $\boldsymbol{A}$ in linear programming
\begin{equation}
\boldsymbol{A} =
\begin{bmatrix}
{1}_n^\top \otimes \mathbb{I}_m \\ \mathbb{I}_n \otimes {1}_m^\top
\end{bmatrix} \in \mathbb{R}^{(m+n)\times mn}
\end{equation}
If the above matrix is partitioned as follows, are the dimensions…
develarist
- 3,009
- 8
- 31
2
votes
1 answer
can we perform sub-gradient updates in mini-batches
We are already aware that in case the data is quite bulky, mini-batch gradient descent based approaches may be applied. These approaches load a mini-batch of data, compute the loss on this batch, and optimize the loss function by updating function…
Upendra01
- 1,566
- 4
- 18
- 28
1
vote
0 answers
`Error: L-BFGS-B needs finite values of 'fn'` of Complex Objective Function
I'm trying to run R's maximum likelihood estimation function (stats4::mle), over a likelihood function in Free Shipping Is Not Free: A Data-Driven Model to Design Free-Shipping Threshold Policies.
Here is the likelihood function I'm trying to run…
nmck160
- 21
- 3
1
vote
0 answers
How do you use pytorch to solve strictly constrained optimization problems?
I am trying to solve the following problem using pytorch: given a six sided die whose average roll is known to be 4.5, what is the maximum entropy distribution for the faces?
(Note: I know a bunch of non-pytorch techniques for solving problems of…
Paul Siegel
- 221
- 1
- 7
1
vote
1 answer
How do linear constraints affect the convexity of my OLS-like optimisation problem?
I would like to augment a linear regression (so a convex OLS problem) with some additional constraints on the coefficients to match the subject I'm working on.
Having $x\in \mathbb{R}^n$, the solution of my linear regression, and my constraints…
quentin
- 11
- 1
1
vote
1 answer
Optimal Feature Engeneering creation: best optimization method?
basically I would like to solve this problem:
(1) say I have N features that I want to transform with a generic f(x, theta) where theta is a continuous bounded variable
(2) I know that each variable has got an optimal different value of theta
(3)…
Asher11
- 189
- 1
- 7
1
vote
0 answers
Solving coefficient sum constrained elastic net with quadratic objective term
I am looking for an algorithm to solve an equality constrained elastic net.
There are two adaptations I need to make to the standard elastic net. First the objective function includes a quadratic term, and second the sum of my coefficients is…
Impatar
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