Questions tagged [continuous-optimization]
The continuous-optimization tag has no summary.
12 questions
0
votes
0
answers
78
views
What's the linearization of the product between a discrete variable and a continuous varibale?
I am trying to linearize the product $z=xy$, where $x$ is an integer variable and $y$ a continuous variable, both non-negative, for an optimization problem. I have tried the SCIP formulation:
$v_{bn} \...
3
votes
2
answers
498
views
Can we use continuous variables instead of binary variables in this NLP problem?
The following problem is defined with binary variables $a_{i1}, a_{i2}, a_{i3}, k_1$ and $k_2$.
Is it possible to avoid binary variables and to only work with continuous variables? How would we ought ...
- 1,073
3
votes
1
answer
66
views
Requesting references about recursive functions where the variables are continuous
I have a recursive function that looks something like this. The variable x is a continuous variable. Do anyone have a reference that looks into a similar problem? $$f_i(y)=\min_{0\le x\le\overline{X_i}...
- 710
3
votes
0
answers
67
views
Help with the KKT conditions of a SPT problem
Could anyone help me with the KKT conditions of my problem? The different sums and sets confuse me more than a little.
$$
\min_x \sum_{a \in A^1} p_a^1 X_a + \sum_{a \in A^2} p_a^2 X_a + \sum_{a \in A^...
- 517
-1
votes
1
answer
162
views
Assignment Problem with continuous decision variable
I have to solve a problem from industry where there are a number of machines which should be assigned to a number of tasks. The difference from the general assignment problem is tough, that the ...
- 49
2
votes
1
answer
144
views
Represent the minimum between two terms as a continuous constraint
Let's consider the following minimization problem:
\begin{align}
\min_{x,a,b}&\quad X\tag1\\
\text{s.t.}&\quad X = \min(A,B)\tag2\end{align}
with $A,B$ functions that depend on $X$.
Is there a ...
- 517
1
vote
1
answer
130
views
LPs having a 'stable' objective value wrt changes in the constraint right-hand sides
I have a problem as:
$$
\begin{align}
\begin{array}{cl}
\underset{x \in \mathbb{R}^n_+}{\min} & c^\top x \\
\mathrm{s.t.} & Ax \leq \mathbf{1} \cdot b ,
\end{array}
\end{align}
$$
where $A \in ...
- 4,050
1
vote
1
answer
127
views
Maximization of a differentiable and nonlinear function over a bounded space
I have a nonlinear bi-variate optimization problem like $\max \: f(x,y)$ where $f(x,y)$ is a nonlinear and differentiable function of both variables, and $0\le x\le 1$, $\:0\le y \le ub$. In order to ...
- 2,170
2
votes
3
answers
383
views
Convex optimization on the unit hypercube with gradients and a bounded minimum
I'd like to find the minimum of a smooth, continuous function inside the unit hypercube (the dimensionality of which could go into the hundreds or even thousands). The function is convex (Hessian $\...
- 123
5
votes
2
answers
249
views
Continuous water-filling optimization problem
Disclaimer: this question has been previously posted on Math StackExchange. I reposted it here since I did not receive any satisfactory answer there and a user suggested to re-post it here.
Let $x\in\...
- 225
9
votes
2
answers
847
views
Which MiniZinc-compatible solvers are best suited for floating decision variables and non-linear constraints?
We are working on a production scheduling problem that has both discrete ("how much to produce from good x and where") and continuous elements ("keep the workload of a production site below 0.7"),
...
- 193
11
votes
1
answer
762
views
Armijo Line Search Parameters
I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
- 4,050