Questions tagged [continuous-optimization]

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11 votes
1 answer

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 ...
3 votes
2 answers

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 ...
3 votes
1 answer

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}...
3 votes
0 answers

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^...
-1 votes
1 answer

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 ...
2 votes
1 answer

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 ...
1 vote
1 answer

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 ...
1 vote
1 answer

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 votes
3 answers

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 $\...
4 votes
2 answers

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\...
9 votes
2 answers

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"), ...